Question

which expression is the factorization of $x^2 + 10x + 21$?
○ $(x + 3)(x + 7)$
○ $(x + 4)(x + 6)$
○ $(x + 6)(x + 15)$
○ $(x + 7)(x + 14)$

Explanation:

Step1: Recall factoring trinomials

To factor \(x^2 + bx + c\), we find two numbers that multiply to \(c\) and add to \(b\). Here, \(b = 10\), \(c = 21\).

Step2: Find numbers for \(21\) and \(10\)

We need two numbers that multiply to \(21\) and add to \(10\). The factors of \(21\) are \(1\&21\), \(3\&7\). \(3 + 7 = 10\), so the factors are \((x + 3)(x + 7)\).

Step3: Verify by expanding

Expand \((x + 3)(x + 7)\): \(x^2 + 7x + 3x + 21 = x^2 + 10x + 21\), which matches the original expression.

Answer:

(x + 3)(x + 7)