Question

what is the factored form of the polynomial?
$x^2 + 9x +20$
$(x - 4)(x - 5)$
$(x - 2)(x - 10)$
$(x + 4)(x + 5)$
$(x + 2)(x + 10)$

Explanation:

Step1: Find pair summing to 9, product 20

We need two numbers that add up to 9 and multiply to 20. These numbers are 4 and 5, since $4+5=9$ and $4\times5=20$.

Step2: Write factored quadratic form

For a quadratic $x^2+bx+c$, the factored form is $(x+m)(x+n)$ where $m+n=b$ and $m\times n=c$. Substitute $m=4$, $n=5$.
<Expression>
$(x+4)(x+5)$
</Expression>

Step3: Verify by expanding

Expand $(x+4)(x+5)$:
$x(x+5)+4(x+5)=x^2+5x+4x+20=x^2+9x+20$, which matches the original polynomial.

Answer:

C. $(x + 4)(x + 5)$