Simply divide.

Very easy if you use Remainder-Factor Theorem.

Let's replace $x$ with $-2$ , ( $(-2) + 2 = 0$ ). Doing this, we get

$(-2)^2 + 5(-2) + 9 = 3$

$3$ is our answer.

Use Synthetic Division.

-2 | 1 5 9

• 0 -2 -6

= 1 3 3

Bring down 1, then multiply it by (-2), then add the product to 5, then multiply it again by (-2), then add to to 9 and the answer will be the remainder. The answer is 3.

(x+2)(x+3)=x^2+5x+6 So the reminder is 3

This is false: If you substitute x for 1, the reaminder is 0, while the rest all have the remainder 3.

Remainder theorem:

F(x) = x^2 + 5x + 9

If (x+2) is a factor, then f(-2) should have remainder zero.

F(-2) = (-2)^2 + 5(-2) + 9

= 4 - 10 + 9

= 3

Therefore the remainder when you divide by (x+2) is 3.

You could also find the answer by doing polynomial division.

first time i tried i got answer by fluke

synthetic division!!!

x+2)x^2+5x+9(x+3

(-)+x^2+2x

     3x+9x

(-)3x+6

    3

so the reminder is 3

remainder theorem x=-2, so -2(-2)+ 5(-2) +9 =4-10+9 =3

$x^{2}$ $+$ $5x$ $+$ $9$

$(-2)^{2}$ $+$ $5(-2)$ $+$ $9$

$4$ $-10$ $+$ $9$

$3$

So, the remainder is 3

we know that x+2 = 0 so x = -2 now substitute x = -2 in x^2+5x+9 i.e 9+4-10 = 3

f(-2)=(-2)*(-2)+5(-2)+9=3