Question

factor the trinomial.
$x^2 + 6x + 5$

Explanation:

Step1: Find two numbers that multiply to 5 and add to 6.

The numbers are 1 and 5, since \(1\times5 = 5\) and \(1 + 5=6\).

Step2: Rewrite the trinomial using these numbers.

We can factor the trinomial as \((x + 1)(x + 5)\) because when we expand \((x + 1)(x + 5)\) using the distributive property (FOIL method), we get \(x^{2}+5x+x + 5=x^{2}+6x + 5\), which matches the original trinomial.

Answer:

\((x + 1)(x + 5)\)