Question

question
factor the trinomial:
$5x^2 + 22x + 21$
answer attempt 1 out of a

Explanation:

Step1: Identify coefficients and constant

For the trinomial \(5x^2 + 22x + 21\), the coefficient of \(x^2\) is \(5\), the coefficient of \(x\) is \(22\), and the constant term is \(21\). We need to find two numbers that multiply to \(5\times21 = 105\) and add up to \(22\).

Step2: Find the two numbers

The numbers \(15\) and \(7\) multiply to \(105\) (\(15\times7 = 105\)) and add up to \(22\) (\(15 + 7 = 22\)).

Step3: Rewrite the middle term

Rewrite \(22x\) as \(15x + 7x\), so the trinomial becomes \(5x^2 + 15x + 7x + 21\).

Step4: Group and factor

Group the first two terms and the last two terms: \((5x^2 + 15x) + (7x + 21)\). Factor out the greatest common factor from each group: \(5x(x + 3) + 7(x + 3)\).

Step5: Factor out the common binomial

Now, factor out the common binomial \((x + 3)\) to get \((5x + 7)(x + 3)\).

Answer:

\((5x + 7)(x + 3)\)