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Exercises Polynomials and factoring

Example 1 from Algebra and Trigonometry, 5.5 Zeros of Polynomial Functions

Using the Remainder Theorem to Evaluate a Polynomial

Use the Remainder Theorem to evaluate $f (x) = 2 x^{5} - 3 x^{4} - 9 x^{3} + 8 x^{2} + 2$ at $x = 2.$

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
To find the remainder using the Remainder Theorem, use synthetic division to divide the polynomial by $x - 2.$

The remainder is 25. Therefore, $f (2) = 25.$

Your turn

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

Use the Remainder Theorem to evaluate $f (x) = 2 x^{5} - 3 x^{4} - 9 x^{3} + 8 x^{2} + 2$ at $x = - 3.$

How did it go?

PreviousUsing Polynomial Division in an Application Problem Next Using the Factor Theorem to Find the Zeros of a Polynomial Expression

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.5, 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.