# Polynomial Inequalities

### Topic Page

Polynomial Inequalities### Questions

- What are common mistakes students make when solving polynomial inequalities?
- How do I solve a polynomial inequality?
- How do I solve the polynomial inequality #-2(m-3)<5(m+1)-12#?
- How do I solve the polynomial inequality #-6<=2(x-5)<7#?
- How do I solve the polynomial inequality #1<2x+3<11#?
- How do I solve the polynomial inequality #-12<-2(x+1)<=18#?
- How do you solve the inequality #6x^2-5x>6#?
- How do you solve #x^2 - 4x - 21<=0# A) [-3, 7] B) (-∞, -3] C) (-∞, -3] [7, ∞) D) [7, ∞)?
- How do you solve quadratic inequality, graph, and write in interval notation #x^2 - 8x + 15 >0#?
- How do you solve #-x^2 - x + 6 < 0#?
- How do you solve #7+13x - 2x^2>0#?
- How do you solve # 10 + x - 2x^2 <0#? c) #-2 + 7x - 3x^2<0#
- How do you solve #-2 + 7x - 3x^2<0#?
- How do you graph #y < x^2- 5x#?
- How do you graph #y > x^2 - 3#?
- How do you solve #y <=-2x^2 + 5x + 6#?
- How do you solve #(x^2-9)*(x^2-16)<=0#?
- How do you solve #–x^2 + 4 < 0#?
- How do you solve #-x^2-4x>3#?
- How do you solve #x^2 + x - 12 > 0#?
- How do you solve inequality #x^2+x+1>0#?
- How do you solve #x^2 -2x ≤ 8#?
- How do you solve #x^2-8x-20<0 #?
- How do you solve #x^2 + 3x - 14 <= 14#?
- How do you solve #12x – 5x < 6(x + 7)#?
- How do you solve #9(3x – 14) > 5(x – 6)#?
- How do you solve quadratic inequalities #4x^2 - 5x < 6#?
- How do you solve the following Quadratic Inequality #x^2+2x-15<0#?
- How do you solve #2(x+3)^2 + 5 > 0#?
- How do you solve #(x + 13)(x - 19)>=0#?
- How do you solve graph #18x-x^2 ≤ 81#?
- How do you solve the quadratic inequality #x^2-9x +18 >0#?
- How do you solve the quadratic inequality #x^2 -4x -5 <0#?
- The total profit function P(x) for a company producing x thousand units is given by #P(x) = -3x^2 + 36x - 81#. How do you find the values of x for which the company makes a profit?
- How do you solve #2x^2 + 7x + 2 >=0#?
- How do you solve and graph #y < 4x^2 - 2x + 1#?
- How do you solve #7+13x - 2x^2>0#?
- How do you solve #10 + x - 2x^2<0#?
- How do you solve #-2 + 7x - 3x^2<0#?
- How do you solve #2p^2 - 7p + 3 > 0#?
- How do you solve #z(2 - z) < z - 12#?
- Question #663d2
- How do you resolve the following inequality: #((x^2-4)(3x-6))/(x-7)>0#?
- How do you solve #6/(3x-4) > x + 1#?
- How do you solve #4x^2 <(12x-9)#?
- How do you solve the inequality and express your answer in interval notation; #x ²-6x+7<0#?
- How do you solve #x(x-1)(x+2)>0#?
- How do you solve #x^3+x^2-16x-16>0#?
- How do you solve #x^4+35x^2-36>=0#?
- How do you solve #x^4-x^2+9<=0#?
- How do you solve #x^4-12x^2+11<0#?
- How do you solve #x^3-216>=0#?
- How do you solve #x^4-13x^2+36<=0#?
- How do you solve #x^3-11x^2-8x+88>=0#?
- How do you solve #x^3+100<0#?
- How do you solve #64x^4-81>0#?
- How do you solve #x^2+2x-3>=0#?
- How do you solve #x^3<9x#?
- How do you solve #x(x-2)^2<0#?
- How do you solve #x^2-2x>=0#?
- How do you solve #25-x^2>=0#?
- How do you solve #(x+3)^2<=0#?
- How do you solve #x(x-3)^2>=0#?
- How do you solve #x^2(4-x)(x+6)<0#?
- How do you solve #x^2+1<=0#?
- How do you solve #x^2-4x>=5#?
- How do you solve #x^4<4x^2#?
- How do you solve #4x^2>12x-9#?
- How do you solve #2x^2-3<=x#?
- How do you solve #7-x^2<=0#?
- How do you solve #x^4-5x^2<=-4#?
- How do you solve #x^5+9x>=10x^3#?
- How do you solve #x^2+9<=0#?
- How do you solve #2x^3-5x^2<2x-5#?
- How do you solve #x^2+2x-3<0#?
- How do you solve #x^3+7x^2+10x>=0#?
- How do you solve #(a-2)(a+4)>0#?
- How do you solve #x^2-9x+8>0#?
- How do you solve #15-2y-y^2<=0#?
- How do you solve #(x+4)(x-2)(x-6)>0#?
- How do you solve #x^3-13x-12<=0#?
- How do you solve #x^4+8x^3+15x^2-4x-20<0#?
- How do you solve #x^4-10x^3+27x^2-2x-40>=0#?
- How do you solve #x^3+x^2-10x+8>=0#?
- How do you solve #4x^2-8x+3<0#?
- How do you solve #(x+1)(x-3)>0#?
- How do you solve #x^2+5x+6>0#?
- How do you solve #x^2-4<=0#?
- How do you solve #4x^2-9x+2<0#?
- How do you solve #2x^2+5x-12>=0#?
- How do you solve #16x^2-81>=0#?
- How do you solve #2x^2+5x-3<=0#?
- How do you solve #13x^2-5x<=0#?
- How do you solve #16x^2<15x+1#?
- How do you solve #x^3+3x^2+x+3<=0#?
- How do you solve #x^3>=x^2#?
- How do you solve #(x+4)(x-2)(x-7)>0#?
- How do you solve #(x-5)^2(x-1)(x+3)<=0#?
- How do you solve #x^3-x^2<9x-9#?
- How do you solve #x^2-10<3x#?
- How do you solve #(x-4)(x+3)<0#?
- How do you solve #(x-4)(x+1)>=0#?
- How do you solve #(x-1)(3x-4)>=0#?
- How do you solve #(x+8)(x+2)(x-3)>=0#?
- How do you solve #x^2+5x+4<=0#?
- How do you solve #x^2-14x+49>=0#?
- How do you solve #x^2-3x-32>0#?
- How do you solve #x^2+16x+24>6x#?
- How do you solve #(x+5)(x-2)(x-1)(x+1)<0#?
- How do you solve #(x+8)^2(x+5)(x+7)^2>=0#?
- How do you solve #x^2+5x+4>0#?
- How do you solve #x^2+x-6>0#?
- How do you solve #x^2-6x+9<0#?
- How do you solve #9x^2+3x-2>=0#?
- How do you solve #2x^2+x<15#?
- How do you solve #6x^2+x>1#?
- How do you solve #4x^2+7x<-3#?
- How do you solve #3x^2+16x<-5#?
- How do you solve #5x<=2-3x^2#?
- How do you solve #4x^2+1>=4x#?
- How do you solve #x^2+2x<0#?
- How do you solve #2x^2+3x>0#?
- How do you solve #-x^2+x>=0#?
- How do you solve #-x^2+2x>=0#?
- How do you solve #9x^2-6x+1<0#?
- How do you solve #4x^2-4x+1>=0#?
- How do you solve #(x-1)(x-2)(x-3)>=0#?
- How do you solve #x(3-x)(x-5)<=0#?
- How do you solve #x(4-x)(x-6)<=0#?
- How do you solve #(5-x)^2(x-13/2)<0#?
- How do you solve #x^3+2x^2-x-2>=0#?
- How do you solve #x^3+2x^2-4x-8>=0#?
- How do you solve #x^3-3x^2-9x+27<0#?
- How do you solve #x^3+7x^2-x-7<0#?
- How do you solve #x^3>=9x^2#?
- How do you solve #x^3<=4x^2#?
- How do you solve #(x-4)/(x+3)>0#?
- How do you solve #(x+5)/(x-2)>0#?
- How do you solve #(x+3)/(x+4)<0#?
- How do you solve #(x+5)/(x+2)<0#?
- How do you solve #(-x+2)/(x-4)>=0#?
- How do you solve #(-x-3)/(x+2)<=0#?
- How do you solve #(4-2x)/(3x+4)<=0#?
- How do you solve #(3x+5)/(6-2x)<=0#?
- How do you solve #x/(x-3)>0#?
- How do you solve #(x+4)/x>0#?
- How do you solve #(x+1)/(x+3)<2#?
- How do you solve #x/(x-1)>2#?
- How do you solve #(x+4)/(2x-1)<=3#?
- How do you solve #(x-2)/(x+2)<=2#?
- How do you solve #x/(x+2)>=2#?
- How do you solve #1/(x+1)>2/(x-1)#?
- How do you solve #(x^2-x-2)/(x^2-4x+3)>0#?
- How do you solve #(x^2-3x+2)/(x^2-2x-3)>0#?
- How do you graph #y>=x^2+2#?
- How do you graph #y<x^2-5x+4#?
- How do you graph #y>=-x^2+3#, #y>=x^2+2x-4#?
- How do you graph #y<=x^2+8x+16#?
- How do you graph #y<x^2-3x#?
- How do you graph #y<=x^2+8x+16#?
- How do you graph #y<x^2-3x#?
- How do you graph #y>=2x^2-2x-5#?
- How do you graph #y>=-2x^2-x+3#?
- How do you graph #y<-1/2x^2-2x+4#?
- How do you graph #y>4/3x^2-12x+29#?
- How do you solve #2x^2-7x+3>=0# by graphing?
- How do you solve #-x^2-2x+8<=0# by graphing?
- How do you solve #-x^2+x+5>0# by graphing?
- How do you solve #3x^2+24x>=-41# by graphing?
- How do you solve #-3/4x^2+4x-8<0# by graphing?
- How do you solve #x^2+3x-18>=0# by algebraically?
- How do you solve #3x^2-16x+5<=0# by algebraically?
- How do you solve #-x^2-12x<32# by algebraically?
- How do you solve #2x^2-4x-5>0# by algebraically?
- How do you solve #1/2x^2+3x<=-6# by algebraically?
- How do you solve #w^2-2<=0# using a sign chart?
- How do you solve #2w^3-8w<0# using a sign chart?
- How do you solve #3w^4-27w^2>0# using a sign chart?
- How do you solve #p^5-p>0# using a sign chart?
- How do you solve #16p^2-81p^6<=0# using a sign chart?
- How do you solve #32p^2-2p^6<0# using a sign chart?
- How do you solve #m^3-2m^2-15m>0# using a sign chart?
- How do you solve #m^4-2m^3-35m^2<=0# using a sign chart?
- How do you solve #y^3-y^2-4y+4>0# using a sign chart?
- How do you solve #y^3-2y^2-9y+18>=0# using a sign chart?
- How do you solve #2y^3-y^2-2+1<=0# using a sign chart?
- How do you solve #(x-4)(x+3)<0# using a sign chart?
- How do you solve #(x-4)(x+1)>=0# using a sign chart?
- How do you solve #(x-1)(3x-4)>=0# using a sign chart?
- How do you solve #(x+8)(x+2)(x-3)>=0# using a sign chart?
- How do you solve #x^2-14x+49>=0# using a sign chart?
- How do you solve #x^2-4x-32>0# using a sign chart?
- How do you solve #x^2+16x+24>6x# using a sign chart?
- How do you solve #(x+5)(x-2)(x-1)(x+1)<0# using a sign chart?
- How do you solve #(x+8)^2(x+5)(x+7)^2>=0# using a sign chart?
- How do you solve #x^2-x-6<=0# using a sign chart?
- How do you solve #2x^2+5x-12>0# using a sign chart?
- How do you solve #2x^3-3x^2-32x+48>=0# using a sign chart?
- How do you solve #(x-3)^2<=1# using a sign chart?
- How do you solve #x^2-6x+9>16# using a sign chart?
- How do you solve #x^4(x-2)>=0# using a sign chart?
- How do you solve #x^2+4x+4>=9# using a sign chart?
- How do you solve #3x^2-11x-4<=0# using a sign chart?
- How do you solve #2x^3+5x^2>6x+9# using a sign chart?
- How do you solve #x^3<x^2# using a sign chart?
- How do you solve #(x-7)(x+3)<=0# using a sign chart?
- How do you solve #x^2-6x+9<0# using a sign chart?
- How do you solve #5x<=2-3x^2# using a sign chart?
- How do you solve #2x^2+3x>0# using a sign chart?
- How do you solve #x^2<=4x-2# using a sign chart?
- How do you solve #(x-1)(x-2)(x-3)<=0# using a sign chart?
- How do you solve #x^3-3x^2-9x+27<0# using a sign chart?
- How do you solve #x^3+x^2+4x+4>0# using a sign chart?
- How do you solve #x^2+2x-15<=0# using a sign chart?
- How do you solve #x^3+4x^2>x+4# using a sign chart?
- How do you solve #x^2-6x+8>=0# using a sign chart?
- How do you solve #-2x^2+10<8x# using a sign chart?
- How do you solve #x^4-10x^2+9>=0# using a sign chart?
- How do you solve #(x+5)^2(x-2)>0# using a sign chart?
- How do you solve #x^2-4x<-3# using a sign chart?
- How do you solve #x^3-6x^2-4x+24>0# using a sign chart?
- How do you solve #((3x-2)(x-4))/(x+4)^2<0# using a sign chart?
- How do you solve #(x-2)(x+1)(x+2)>0# using a sign chart?
- How do you solve #(x-3)^2(2x+1)<=0# using a sign chart?
- How do you solve #(x-4)^5(x-5)(x+3)<0# using a sign chart?
- How do you solve #(x-1)(x-2)(x-3)>=0# using a sign chart?
- How do you solve #-x^4-16>0# using a sign chart?
- How do you solve #x^3+3x^2<4# using a sign chart?
- How do you solve #x^3-5x^2<x-5# using a sign chart?
- How do you solve #2x^3+x^2-5x+2<=0# using a sign chart?
- How do you solve #(x+1)(x-7)<=0# using a sign chart?
- How do you solve #9x^2+3x-2>=0# using a sign chart?
- How do you solve #3x^2<5x# using a sign chart?
- How do you solve #x^3+2x^2-4x-8>=0# using a sign chart?
- How do you solve #x^3<=4x^2# using a sign chart?
- How do you solve #(x-6)(x+10)<0#?
- How do you solve #(x-8)(x+3)>0#?
- How do you solve #(x+5)(x-2)>=0#?
- How do you graph the inequality #y>=x^2-10x+25#?
- How do you graph the inequality #y<x^2-16#?
- How do you graph the inequality #y> -2x^2-4x+3#?
- How do you graph the inequality #y<=-x^2+5x+6#?
- How do you solve the inequality #x^2-6x-7<0#?
- How do you solve the inequality #x^2-x-12>0#?
- How do you solve the inequality #x^2<10x-25#?
- How do you graph the inequality #y>=x^2+3x-18#?
- How do you graph the inequality #y<=x^2+4x#?
- How do you graph the inequality #y>x^2-36#?
- How do you graph the inequality #y<=-x^2-3x+10#?
- How do you graph the inequality #y>=-x^2-7x+10#?
- How do you graph the inequality #y> -x^2+10x-23#?
- How do you graph the inequality #y<-x^2+13x-36#?
- How do you graph the inequality #y<2x^2+3x-5#?
- How do you graph the inequality #y>=2x^2+x-3#?
- How do you solve the inequality #x^2-3x-18>0#?
- How do you solve the inequality #x^2+3x-28<0#?
- How do you solve the inequality #x^2-4x<=5#?
- How do you solve the inequality #x^2+2x>=24#?
- How do you solve the inequality #-x^2-6x+7<=0#?
- How do you solve the inequality #9x^2-6x+1<=0#?
- How do you solve the inequality #4x^2+20x+25>=0#?
- How do you solve the inequality #x^2+12x<-36#?
- How do you solve the inequality #-x^2+14x-49>=0#?
- How do you solve the inequality #18x-x^2<=81#?
- How do you solve the inequality #16x^2+9<24x#?
- How do you solve the inequality #(x-1)(x+4)(x-3)>0#?
- How do you graph #0<=x-y<=2#?
- How do you determine if (-1,-3) is a solution to #y>=-5x^4+7x^3+8#?
- How do you determine if (0,3) is a solution to #y<abs(3x-4)#?
- How do you graph #y<=(x+1)^3#?
- How do you solve #abs(x+6)>4#?
- How do you solve #abs(3x-4)<=x#?
- How do you determine whether the pair (1,0) is a solution to #y<x^3-4x^2+2#?
- How do you determine whether the pair (3,8) is a solution to #y<abs(x-2)#?
- How do you determine whether the pair (-2,-1) is a solution to #y> -sqrt(x+11)+1#?
- How do you determine whether the pair (10,63) is a solution to #y< -0.2x^2+9x-7#?
- How do you determine whether the pair (-6,-9) is a solution to #y<= (x^2-6)/x#?
- How do you graph the inequality #y<=x^2-4#?
- How do you graph the inequality #y<abs(x-9)#?
- How do you graph the inequality #y<(x-5)^2#?
- How do you graph the inequality #y>=-x^3#?
- How do you graph the inequality #y<sqrt(x+3)+5#?
- How do you graph the inequality #y>=(x-1)^2-3#?
- How do you graph the inequality #y<=-3abs(x-2)+4#?
- How do you graph the inequality #y>=x^3-6x^2+12x-8#?
- How do you graph the inequality #y>=x^3-6x^2+12x-8#?
- How do you solve #abs(x+4)>5#?
- How do you solve #abs(3x+12)>=42#?
- How do you solve #abs(7-2x)-8<3#?
- How do you solve #abs(5-x)<=x#?
- How do you solve #abs(5x-8)<0#?
- How do you solve #abs(2x+9)-2x>=0#?
- How do you solve the inequality #2x^2+9x+3<=0#?
- How do you solve the inequality #2x^2+25x+63<=0#?
- How do you solve #x(x-1)(x+3) <0#?
- What is the solution set of the quadratic inequality #x^2-5<=0#?
- How do you solve #sqrt(2x-7)>=5#?
- How do you solve #sqrt(b+4)<=6#?
- How do you solve #sqrt(a-5)<=4#?
- How do you solve #sqrt(2x-5)<=6#?
- How do you solve #sqrt(m+2)<sqrt(3m+4)#?
- How do you solve #5^x>=625#?
- Which of the following points is in the solution set of #y> -x^2+5#?
- How do you solve #x^2+4x+3<=0#?
- How do you solve #x^2+2x>0#?
- How do you solve #x^2+2x<0#?
- How do you solve #n^2+2n-24<=0#?
- How do you solve #n^2+2n-24>0#?
- How do you solve #-s^2+4s-6<0#?
- How do you solve #-s^2+4s-6>0#?
- How do you solve #8r-r^2>=15#?
- How do you solve #3x^2-5x>8#?
- How do you solve #z^2-6z+7<2#?
- How do you solve #-p^2+10p-7<=14#?
- How do you solve the inequality #x^2+2x-3>=0# and write your answer in interval notation?
- How do you solve the inequality #16x^2+8x+1>0# and write your answer in interval notation?
- How do you solve the inequality #x^2+9<6x# and write your answer in interval notation?
- How do you solve the inequality #9x^2+16>=24x# and write your answer in interval notation?
- How do you solve the inequality #x^2+4<=4x# and write your answer in interval notation?
- How do you solve the inequality #x^2+1<0# and write your answer in interval notation?
- How do you solve the inequality #3x^2<=11x+4# and write your answer in interval notation?
- How do you solve the inequality #x>x^2# and write your answer in interval notation?
- How do you solve the inequality #2x^2-4x-1>0# and write your answer in interval notation?
- How do you solve the inequality #5x+4<=3x^2# and write your answer in interval notation?
- How do you solve the inequality #2<=abs(x^2-9)<9# and write your answer in interval notation?
- How do you solve the inequality #x^2<=abs(4x-3)# and write your answer in interval notation?
- How do you solve the inequality #x^2+x+1>=0# and write your answer in interval notation?
- How do you solve the inequality #x^2>=absx# and write your answer in interval notation?
- How do you solve the polynomial inequality and state the answer in interval notation given #4x^4>=3x+1#?
- How do you solve the polynomial inequality and state the answer in interval notation given #x^4<=16+4x-x^3#?
- How do you solve the polynomial inequality and state the answer in interval notation given #3x^2+2x<x^4#?
- How do you solve the polynomial inequality and state the answer in interval notation given #(x^3+2x^2)/2<x+2#?
- How do you solve the polynomial inequality and state the answer in interval notation given #(x^3+20x)/8>=x^2+2#?
- How do you solve the polynomial inequality and state the answer in interval notation given #2x^4>5x^2+3#?
- How do you solve the polynomial inequality and state the answer in interval notation given #x^6+x^3>=6#?
- How do you solve the exponential inequality #4^x<=4^(3x-1)#?
- How do you solve the exponential inequality #9^(2x-3)<=9^(x+2)#?
- How do you solve the exponential inequality #2^(x+3)<=16^(4x-2)#?
- How do you solve the exponential inequality #2^(4x)>=8^(x+5)#?
- How do you solve the exponential inequality #5^(2x+2)>=25^(2x-3)#?
- How do you solve the exponential inequality #3^(x-2)<=3^(2x+4)#?
- How do you solve the exponential inequality #8^(2x)>=8^(x+7)#?
- How do you solve the exponential inequality #5^(x-4)<=25^(x-6)#?
- How do you solve the exponential inequality #8^(x-1)<=32^(3x-2)#?
- How do you solve the exponential inequality #27^(4x-1)>=9^(3x+8)#?
- Solve the inequality and specify any excluded values? #-2 < (3x+1)/(x-3)#
- Question #65677
- Prove that #\sqrt{ \frac{2x^2 - 2x + 1}{2} } \geq \frac{1}{x + \frac{1}{x}}#for #0 < x < 1.# ?