Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - 11-3 Dividing Polynomials - Practice and Problem-Solving Exercises - Page 669: 18



Work Step by Step

In order to match the first term of the dividend, $3x^2$, the divisor $(x-3)$ must be multiplied by $3x$. The $3x$ will go on top of your division sign. $$(3x)(x-3) = 3x^2-9x$$ Then, subtract this from the first two terms of the dividend. $$(3x^2-10x+3) - (3x^2 - 9x) = -x$$ Bring down the next term of the dividend. $$-x+3$$ Multiply the divisor by $(-1)$ to match this. The $-1$ will follow the $3x$ on top of your division sign. $$(-1)(x-3) = (-x+3)$$ Subtract this from the dividend. Since this results in zero, you have no remainder and a final answer of $(3x-1)$
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