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Exercises Polynomials and factoring

Example 6.82 from Elementary Algebra, 6.6 Divide Polynomials

Divide Polynomials: example 6.82

Find the quotient: $\frac{36 x^{3} y^{2} + 27 x^{2} y^{2} - 9 x^{2} y^{3}}{9 x^{2} y} .$

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

$\frac{36 x^{3} y^{2} + 27 x^{2} y^{2} - 9 x^{2} y^{3}}{9 x^{2} y}$

Separate the terms. $\frac{36 x^{3} y^{2}}{9 x^{2} y} + \frac{27 x^{2} y^{2}}{9 x^{2} y} - \frac{9 x^{2} y^{3}}{9 x^{2} y}$

Simplify. $4 x y + 3 y - y^{2}$

Your turn

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

Find the quotient: $\frac{40 x^{3} y^{2} + 24 x^{2} y^{2} - 16 x^{2} y^{3}}{8 x^{2} y} .$

How did it go?

PreviousDivide Polynomials: example 6.81 Next Divide Polynomials: example 6.83

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 6.6, 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.