Question

What is the remainder when 3x^3-14x^2-14x+3 is divided by 3x + 5

Answer 1

Answer:

${- \frac{238}{9}}$

Step-by-step explanation:

We want to find the remainder when the polynomial

$p(x) = 3 {x}^{3} - 14 {x}^{2} - 14x + 3$

is divided by 3x+5.

According to the remainder theorem, a polynomial p(x) is divided by ax+b, then the remainder is given by

$R(x) = p( - \frac{b}{a})$

We substitute x=-5/3 to get:

$p( - \frac{5}{3} ) = 3 {(- \frac{5}{3})}^{3} - 14 {(- \frac{5}{3})}^{2} - 14 \times - \frac{5}{3}+ 3$

We now simplify to obtain:

$p( - \frac{5}{3} ) = 3 {(- \frac{125}{27})} - 14 {( \frac{25}{9})} + \frac{70}{3}+ 3$

This simplifies to:

$p( - \frac{5}{3} ) = - \frac{125}{9} - { \frac{350}{9}} + \frac{70}{3}+ 3$

$p( - \frac{5}{3} ) = {- \frac{238}{9}}$

Therefore the remainder is -238/9