Answered: h h + 7 2h

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.5: The Distributive Property

Problem 22WE

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Question

Solve; a. Use synthetic division to show that 2 is a solution of the polynomial equation 2h³ + 14h² - 72 = 0.

b. Use the solution from part (a) to solve this problem. The width of a rectangular box is twice the height and the length is 7 inches more than the height. If the volume is 72 cubic inches, find the dimensions of the box.

Expert Solution

Step 1

a. Use synthetic division to show that 2 is a solution of the polynomial equation 2h³ + 14h² - 72 = 0.

Step 2

Verify that 2 is a solution of the equation.

If the function is divided by factor $x - c$ , then the remainder becomes 0.

Substitute 2 for c in $h - c$ .

$h - 2 2 h^{2} h + 3 2 h^{3} + 14 h^{2} - 72 2 h^{3} - 4 h^{2} 18 h^{2} - 72 18 h^{2} - 36 h 36 h - 72 36 h - 72 0$

Here, the remainder is 0, so $h - 2$ is the factor of the equation.

Hence, 2 is a solution of the equation.

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