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Exercises Polynomials and factoring

Example 5 from Algebra and Trigonometry, 5.4 Dividing Polynomials

Using Synthetic Division to Divide a Fourth-Degree Polynomial

Use synthetic division to divide $- 9 x^{4} + 10 x^{3} + 7 x^{2} - 6$ by $x - 1.$

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
Notice there is no x-term. We will use a zero as the coefficient for that term.

The result is $- 9 x^{3} + x^{2} + 8 x + 8 + \frac{2}{x - 1} .$

Your turn

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

Use synthetic division to divide $3 x^{4} + 18 x^{3} - 3 x + 40$ by $x + 7.$

How did it go?

PreviousUsing Synthetic Division to Divide a Third-Degree Polynomial Next Using Polynomial Division in an Application Problem

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.