Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.6 - Solving Quadratic Equations by Factoring - Exercise Set - Page 473: 58


$x=5$ or $x=1$ or $x=2$

Work Step by Step

$(x-5)(x^{2}-3x+2)=0\qquad$...apply the principle of zero products. First part: $x-5=0$ $x=5$ Second part: $x^{2}-3x+2=0$ ... Searching for two factors of $ac=2$ whose sum is $b=-3,$ we find$\qquad-1$ and $-2.$ Rewrite the middle term and factor in pairs: $x^{2}-x-2x+2=0$ $x(x-1)-2(x-1)=0$ $(x-1)(x-2)=0\qquad$...apply the principle of zero products. $x-1=0$ or $x-2=0$ $x=1$ or $x=2$ Type the equation into a graphing utility and see that the graph intercepts the x-axis at $1,2$ and $5$.
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