How do you divide 3x^3+5x^2+2x-123x3+5x2+2x12 by x+3x+3?

2 Answers

p(x)=3x^2-4x+14+((-54))/(x+3)p(x)=3x24x+14+(54)x+3

Explanation:

Let 3x^3+5x^2+2x-123x3+5x2+2x12 be p(x)p(x)
Using long division of polynomial's
(+)3x^2-4x+14(+)3x24x+14
root(x+3)(3x^3+5x^2+2x-12)x+33x3+5x2+2x12
((-)3x^3+9x^2)/(-4x^2+2x-12)()3x3+9x24x2+2x12
((-)-4x^2-12x)/(14x-12)()4x212x14x12
((-)14x+42)/-54()14x+4254
p(x)=Q(x)+(R)/Dp(x)=Q(x)+RD
Where,Q=Q=quotient
R=R=remainder
D=D=divisor
=>p(x)=3x^2-4x+14+((-54))/(x+3)p(x)=3x24x+14+(54)x+3

Apr 7, 2018

3x^2-4x+14-54/(x+3)3x24x+1454x+3

Explanation:

"one way is to use the divisor as a factor in the numerator"one way is to use the divisor as a factor in the numerator

"consider the numerator"consider the numerator

color(red)(3x^2)(x+3)color(magenta)(-9x^2)+5x^2+2x-123x2(x+3)9x2+5x2+2x12

=color(red)(3x^2)(x+3)color(red)(-4x)(x+3)color(magenta)(+12x)+2x-12=3x2(x+3)4x(x+3)+12x+2x12

=color(red)(3x^2)(x+3)color(red)(-4x)(x+3)color(red)(+14)(x+3)color(magenta)(-42)-12=3x2(x+3)4x(x+3)+14(x+3)4212

=color(red)(3x^2)(x+3)color(red)(-4x)(x+3)color(red)(+14)(x+3)-54=3x2(x+3)4x(x+3)+14(x+3)54

"quotient "=color(red)(3x^2-4x+14)," remainder "=-54quotient =3x24x+14, remainder =54

rArr3x^3+5x^2+2x-123x3+5x2+2x12

=3x^2-4x+14-54/(x+3)=3x24x+1454x+3