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 - Page 212: 10

Answer

True

Work Step by Step

$\frac{-30x^{5}+20x^{4} -10x^{3}}{-5x^{2}}$ = 6$x^{3}$ - 4$x^{2}$ + 2x To check if this is true or not, we simplify the left side. RECALL: $\frac{b^{n}}{b^{m}}$ = $b^{n-m}$ So, $\frac{-30x^{5}+20x^{4} -10x^{3}}{-5x^{2}}$ = $\frac{-30x^{5}}{-5x^{2}}$ + $\frac{20x^{4}}{-5x^{2}}$ + $\frac{-10x^{3}}{-5x^{2}}$ = $\frac{-30}{-5}$$x^{5-2}$ + $\frac{20}{-5}$$x^{4-2}$ + $\frac{-10}{-5}$$x^{3-2}$ = 6$x^{3}$ - 4$x^{2}$ + 2x Because 6$x^{3}$ - 4$x^{2}$ + 2x is equal to 6$x^{3}$ - 4$x^{2}$ + 2x, this statement is true.
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