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Exercises Polynomials and factoring

Example 2 from Algebra and Trigonometry, 5.4 Dividing Polynomials

Using Long Division to Divide a Third-Degree Polynomial

Divide $6 x^{3} + 11 x^{2} - 31 x + 15$ by $3 x - 2.$

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

There is a remainder of 1. We can express the result as:

$\frac{6 x^{3} + 11 x^{2} - 31 x + 15}{3 x - 2} = 2 x^{2} + 5 x - 7 + \frac{1}{3 x - 2}$

Your turn

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

Divide $16 x^{3} - 12 x^{2} + 20 x - 3$ by $4 x + 5.$

How did it go?

PreviousUsing Long Division to Divide a Second-Degree Polynomial Next Using Synthetic Division to Divide a Second-Degree Polynomial

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.4, 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.