Question

The binomial (x+2) is a factor of ?

1). 2x^{2} -5+3
2). x^{2} +5x+18
3). x^{3} +5x^{2} + 18
4). x^{3} +5x+18

Answer 1

4).
`x^(3) +5x+18`

Explanation:

The binomial (x+2) is a factor of
`x^(3) +5x+18.`

Since, (x + 2) is a factor.

So, x = - 2 is a root

Plug x = - 2 in
`x^(3) +5x+18`

We find:

`x^(3) +5x+18`

`=(-2)^(3) +5(-2)+18`

`=-8 - 10+18`

`= - 18+18`

`= 0`

Since, at x = - 2 the value of the expression
`x^(3) +5x+18` becomes zero.

Therefore, (x + 2) is a factor of
`x^(3) +5x+18`