Question

What is the remainder when the polynomial 5x2+10x−15 is divided by x + 5? Enter your answer in the box.

Answer 1

There are two ways you can approach this:

1) Factor $\frac{5(x-1)(x+3)}{x+5}$ this equals to $\frac{5x^2+10x-15}{x+5}$

2) or divide which equals to 5x+35+$\frac{160}{x+5}$

Answer 2

ANSWER
The remainder is
$60$

EXPLANATION

Let

$p(x) = 5 {x}^{2} + 10x - 15$

We shall apply the remainder theorem to obtain the remainder when
$p(x)$
is divided by
$x + 5$

According to the remainder theorem, if a polynomial
$p(x)$
is divided by
$x - a$
then the remainder is
$p(a)$


So we set
$x + 5 = 0$

and solve for
$x$

to obtain,

$x = - 5$


We now substitute -5 into the given polynomial to find the remainder.



$p( - 5) = 5 {( - 5)}^{2} + 10( - 5) - 15$


This gives us,

$p( - 5) = 5(25) - 50 - 15$

This will simplify to,

$p( - 5) = 125 - 50 - 15$



$p( - 5) = 60$


Therefore the remainder is
$60$