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
`(5(x-1)(x+3))/(x+5)` this equals to
`(5x^2+10x-15)/(x+5)`

2) or divide which equals to 5x+35+
`(160)/(x+5)`

Answer 2

ANSWER
The remainder is

`60`

Step-by-step 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`