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Factorize 2b2 - 10b + 12

June 22, 2026Mathematics

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Answer

2(b - 2)(b - 3)

4 steps

Here's the step-by-step solution for factoring the quadratic expression:

Identify the coefficients and find two numbers that multiply to $a \times c$ and add to $b$ .
For $2b^2 - 10b + 12$ , we have $a=2$ , $b=-10$ , $c=12$ .
We need two numbers that multiply to $2 \times 12 = 24$ and add up to $-10$ . These numbers are $-6$ and $-4$ .
Rewrite the middle term using the two numbers found in Step 1.
$2b^2 - 6b - 4b + 12$
Group the terms and factor out the greatest common factor (GCF) from each pair.
$2b(b - 3) - 4(b - 3)$
Factor out the common binomial factor.
$(2b - 4)(b - 3)$
Notice that $2b-4$ can be further factored by taking out a GCF of 2.
$2(b - 2)(b - 3)$

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