Question

factor the quadratic expression ( a^2 + 9a + 20 ). the options are: ((a + 10)(a + 2)), ((a + 4)(a + 5)), (a(a^2 + 9a + 20)), ((a + 10)(a - 2))

Explanation:

Step1: Find factors of 20 that sum to 9

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

Step2: Factor the quadratic expression

Use the two numbers to write the factored form of $a^2+9a+20$.
$a^2+9a+20=(a+4)(a+5)$

Step3: Verify by expanding

Check by multiplying the factors:
$(a+4)(a+5)=a^2+5a+4a+20=a^2+9a+20$, which matches the original expression.

Answer:

B. $(a + 4)(a + 5)$