Question

1. factor the trinomial.

$7x^2 + 9x + 2$
$7x^2 + 9x + 2 = \boxed{\quad}$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(7\times2 = 14\) and add up to \(9\). The numbers are \(7\) and \(2\) since \(7\times2 = 14\) and \(7 + 2=9\).

Step2: Split the middle term

Rewrite the middle term \(9x\) as \(7x+2x\) in the trinomial: \(7x^{2}+7x + 2x+2\).

Step3: Group and factor

Group the first two terms and the last two terms: \((7x^{2}+7x)+(2x + 2)\). Factor out the greatest common factor from each group: \(7x(x + 1)+2(x + 1)\).

Step4: Factor out the common binomial

Now, factor out the common binomial \((x + 1)\): \((7x + 2)(x + 1)\).

Answer:

\((7x + 2)(x + 1)\)