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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 480 (page 562)

In the following exercises, use synthetic division to find the quotient and remainder.
$x^{4} + x^{2} + 6 x - 10$ is divided by $x + 2$

Short Answer

Expert verified

The quotient is $x^{3} - 2 x^{2} + 5 x - 4$ and the remainder is $- 2$ .

Step by step solution

01

Step 1. Given information.

It is given that,

Dividend: $x^{4} + x^{2} + 6 x - 10$

Divisor: $x + 2$

In the given dividend there is no term. So, the given dividend can be written as:

$x^{4} + 0 x^{3} + x^{2} + 6 x - 10$

02

Step 2. Divide polynomials using synthetic division

Write the coefficients of the dividend in the first row of the synthetic division and write the divisor as $x - c$ and place $c$ in the synthetic division in the divisor box.

$- 2 1 0 1 6 - 10 - 2 4 - 10 8 1 - 2 5 - 4 - 2$

The numbers in the third row give us the result. The last digit in the third row represents the remainder and the other digits are the coefficients of the quotient.

Quotient $= x^{3} - 2 x^{2} + 5 x - 4$

Remainder $= - 2$

03

Step 3. Conclusion.

The quotient is $x^{3} - 2 x^{2} + 5 x - 4$ and the remainder is $- 2$ .

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