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Exercises Polynomials and factoring

Example 7.8 from Elementary Algebra, 7.1 Greatest Common Factor and Factor by Grouping

Greatest Common Factor and Factor by Grouping: example 7.8

Factor: $4 y^{2} + 24 y + 28$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We start by finding the GCF of all three terms.

Find the GCF of $4 y^{2}$ , $24 y$ and 28.

Rewrite each term as a product using the GCF.

Factor the GCF.

Check by mulitplying.

$4 (y^{2} + 6 y + 7)$

$4 \cdot y^{2} + 4 \cdot 6 y + 4 \cdot 7$

$4 y^{2} + 24 y + 28 ✓$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor: $5 x^{2} - 25 x + 15$ .

How did it go?

PreviousGreatest Common Factor and Factor by Grouping: example 7.6 Next Greatest Common Factor and Factor by Grouping: example 7.9

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 7.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.