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Exercises Expressions, exponents and radicals

Example 1 from Algebra and Trigonometry, 1.5 Factoring Polynomials

Factoring the Greatest Common Factor

Factor $6 x^{3} y^{3} + 45 x^{2} y^{2} + 21 x y .$

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
First, find the GCF of the expression. The GCF of 6, 45, and 21 is 3. The GCF of $x^{3}, x^{2}$ , and $x$ is $x$ . (Note that the GCF of a set of expressions in the form $x^{n}$ will always be the exponent of lowest degree.) And the GCF of $3 x y (7) = 21 x y .$ , and $y$ is $y$ . Combine these to find the GCF of the polynomial, $3 x y$ .
Next, determine what the GCF needs to be multiplied by to obtain each term of the polynomial. We find that $3 x y (2 x^{2} y^{2}) = 6 x^{3} y^{3}, 3 x y (15 x y) = 45 x^{2} y^{2}$ , and $3 x y (7) = 21 x y .$
Finally, write the factored expression as the product of the GCF and the sum of the terms we needed to multiply by.

$(3 x y) (2 x^{2} y^{2} + 15 x y + 7)$

Your turn

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

Factor $x (b^{2} - a) + 6 (b^{2} - a)$ by pulling out the GCF.

How did it go?

PreviousMultiplying Polynomials Containing Several Variables Next Factoring a Trinomial with Leading Coefficient 1

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.5, 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.