How do you divide 3x^3+5x^2+2x-12 by x+3?

2 Answers

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

Explanation:

Let 3x^3+5x^2+2x-12 be p(x)
Using long division of polynomial's
(+)3x^2-4x+14
root(x+3)(3x^3+5x^2+2x-12)
((-)3x^3+9x^2)/(-4x^2+2x-12)
((-)-4x^2-12x)/(14x-12)
((-)14x+42)/-54
p(x)=Q(x)+(R)/D
Where,Q=quotient
R=remainder
D=divisor
=>p(x)=3x^2-4x+14+((-54))/(x+3)

Apr 7, 2018

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

Explanation:

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

"consider the numerator"

color(red)(3x^2)(x+3)color(magenta)(-9x^2)+5x^2+2x-12

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

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

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

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

rArr3x^3+5x^2+2x-12

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