Here's the step-by-step solution for factoring the quadratic expression 3f² + 2f − 1: Step 1: Identify the coefficients and find two numbers that multiply to a × c and add to b. For 3f² + 2f − 1, we have a=3, b=2, c=−1. We need two numbers that multiply to a × c = 3 × (−1) = −3 and add up to b = 2. These numbers are 3 and −1. Step 2: Rewrite the middle term using the two numbers found in Step 1. 3f² + 3f − 1f − 1 Step 3: Group the terms and factor out the greatest common factor (GCF) from each pair. 3f(f + 1) − 1(f + 1) Step 4: Factor out the common binomial factor. (3f − 1)(f + 1) The final factored expression is: (3f − 1)(f + 1)

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2b2 + 2b - 1

June 22, 2026Mathematics

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Answer

(3f - 1)(f + 1)

Step-by-step solution

4 steps

Here's the step-by-step solution for factoring the quadratic expression $3f^2 + 2f - 1$ :

Identify the coefficients and find two numbers that multiply to $a \times c$ and add to $b$ .
For $3f^2 + 2f - 1$ , we have $a=3$ , $b=2$ , $c=-1$ .
We need two numbers that multiply to $a \times c = 3 \times (-1) = -3$ and add up to $b = 2$ . These numbers are 3 and $-1$ .
Rewrite the middle term using the two numbers found in Step 1.
$3f^2 + 3f - 1f - 1$
Group the terms and factor out the greatest common factor (GCF) from each pair.
$3f(f + 1) - 1(f + 1)$
Factor out the common binomial factor.
$(3f - 1)(f + 1)$

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2b2 + 2b - 1

Answer

Step-by-step solution

Identify the coefficients and find two numbers that multiply to a×ca \times ca×c and add to bbb.

Rewrite the middle term using the two numbers found in Step 1.

Group the terms and factor out the greatest common factor (GCF) from each pair.

Factor out the common binomial factor.

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More Mathematics Questions

Identify the coefficients and find two numbers that multiply to $a \times c$ and add to $b$ .