Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.4 - Dividing by Monomials - Concept Quiz 5.4: 9

Answer

True

Work Step by Step

$\frac{24x^{6}-18x^{4} +12x^{2}}{2x^{2}}$ = 12$x^{4}$ - 9$x^{2}$ + 6 To check if this is true or not, we simplify the left side. RECALL: $\frac{b^{n}}{b^{m}}$ = $b^{n-m}$ So, $\frac{24x^{6}-18x^{4} +12x^{2}}{2x^{2}}$ = $\frac{24x^{6}}{2x^{2}}$ - $\frac{18x^{4}}{2x^{2}}$ + $\frac{12x^{2}}{2x^{2}}$ = $\frac{24}{2}$$x^{6-2}$ - $\frac{18}{2}$$x^{4-2}$ + $\frac{12}{2}$$x^{2-2}$ = 12$x^{4}$ - 9$x^{2}$ + 6 Because 12$x^{4}$ - 9$x^{2}$ + 6 is equal to 12$x^{4}$ - 9$x^{2}$ + 6, this statement is true.
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