Solve in brief 3x square - x-4??

2 Answers
Apr 26, 2018

(3x-4)(x+1)

Explanation:

(This is a method my teacher developed; it gives the right answer but you should know the other ways to do it before start learning this method)

3x^2-x-4 -> ax^2+bx+c

Multiply the c by the coefficient of x^2

x^2-x-12

Then, find the factors that make -12 and add up to -1.

(x-4)(x+3)

Put the coefficient of x^2 back into each bracket and simplify.

(3x-4)(3x+3) -> (3x-4)(x+1)

3x^2-x-4 = (3x-4)(x+1)

Apr 26, 2018

x=4/3" or "x=-1

Explanation:

"to solve the quadratic equate to zero and factor"

rArr3x^2-x-4=0

"using the a-c method of factoring"

"the factors of the product "3xx-4=-12

"which sum to - 1 are + 3 and - 4"

"split the middle term using these factors"

3x^2+3x-4x-4=0larrcolor(blue)"factor by grouping"

color(red)(3x)(x+1)color(red)(-4)(x+1)=0

"take out the "color(blue)"common factor "(x+1)

rArr(x+1)(color(red)(3x-4))=0

"equate each factor to zero and solve for x"

x+1=0rArrx=-1

3x-4=0rArrx=4/3