Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 5 - Polynomials and Polynomial Functions - 5-4 Dividing Polynomials - Practice and Problem-Solving Exercises - Page 309: 54

Answer

$x-1$ is a factor

Work Step by Step

The picture below shows the result of $( 3x^3+10x^2-x-12 )\div( x-1 )$ using synthetic division. The numbers in the last row in the picture below are the coefficients of the quotient and the remainder. In that row, the left-most number is the coefficient of $ x^3 $ (leading term of dividend) divided by $ x $ (leading term of divisor). Since $ x^3\div x=x^2 ,$ then the left-most number is the coefficient of $ x^2 $ and the next numbers are the coefficients of $x$ in decreasing exponent (down to exponent $0$). The right-most number, on the other hand, represents the remainder. Since the remainder is $0,$ then $ x-1 $ is a factor of $ 3x^3+10x^2-12 .$
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