Question

factor ( z^2 + 10z + 21 ). the factored expression is (square).

Explanation:

Step1: Find two numbers that multiply to 21 and add to 10.

We need two numbers \(a\) and \(b\) such that \(a \times b = 21\) and \(a + b = 10\). The numbers 3 and 7 work because \(3 \times 7 = 21\) and \(3 + 7 = 10\).

Step2: Factor the quadratic expression.

Using the numbers found, we can factor \(z^{2}+10z + 21\) as \((z + 3)(z + 7)\) since \((z + 3)(z + 7)=z^{2}+7z+3z + 21=z^{2}+10z + 21\).

Answer:

\((z + 3)(z + 7)\)