Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.4 - Division of Polynomials - Exercise Set - Page 446: 79

Answer

$(x-2)$.

Work Step by Step

The dividend is $2x^2-7x+9$. The quotient is $2x-3$. The remainder is $3$. The divisor is $= \frac{dividend -remainder}{quotient} $ Substitute all values. The divisor is $= \frac{2x^2-7x+9 -3}{2x-3} $ Simplify. The divisor is $= \frac{2x^2-7x+6}{2x-3} $ $\begin{matrix} & x & -2 & & & \leftarrow &Quotient\\ &-- &-- &--&--& \\ 2x-3) &2x^2&-7x&+6 & \\ & 2x^2 & -3x & & & \leftarrow &x(2x-3) \\ & -- & -- & & & \leftarrow &subtract \\ & 0 & -4x & +6 & & \\ & & -4x & +6 & & \leftarrow & -2(2x-3) \\ & & -- & -- & & \leftarrow & subtract \\ & & 0&0 & & \leftarrow & Remainder \end{matrix}$ Hence, the divisor is $(x-2)$.
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