factor the polynomial:

x^2 + 6x + 9

Try a perfect square:

(x+a)²
=x²+2ax+a²

x^2+6x+9

Product of the coefficients of the 1st and last terms: +9 (1x9)
Sum: +6 (middle term is always the sum)

List all the factors of 9 and determine which pair would give you a product of +9 and a sum of +6:
1,9
3,3 ✓

your answer will be (x+3)^2 or (x+3)(x+3)

Check: F.O.I.L. (x+3)(x+3)
x^2+3x+3x+9
x^2+6x+9

To factor the polynomial x^2 + 6x + 9, we need to find two binomials that, when multiplied together, will give us the original polynomial.

The first term will be the square root of the coefficient of the x^2 term, which is x.
The last term will be the square root of the constant term, which is 3.

So, the factors of the polynomial x^2 + 6x + 9 will be:
(x + 3)(x + 3) or (x + 3)^2

This is because when we multiply (x + 3) by itself, we get x^2 + 6x + 9.

Therefore, the factored form of x^2 + 6x + 9 is (x + 3)^2.