Question

factor.
$x^2 + 10x + 21$

Explanation:

Step1: Find pair summing to 10, product 21

We need two numbers that add up to 10 and multiply to 21. These numbers are 3 and 7, since $3+7=10$ and $3\times7=21$.

Step2: Rewrite trinomial as factored form

Use the two numbers to write the quadratic as a product of two binomials:
$x^2 + 10x + 21 = (x+3)(x+7)$

Answer:

$(x+3)(x+7)$