College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.5 - Factoring Polynomials - R.5 Exercises: 85

Answer

$(x-7)(x-3)$

Work Step by Step

RECALL: A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$. The trinomial's factored form will be: $x^2+bx+c=(x+d)(x+e)$ The given trinomial has $b=-10$ and $c=21$. Note that $21=(-7)(-3)$ and $-10= (-7)+(-3)$. This means that $d=-7$ and $e=-3$ Thus, the factored form of the trinomial is: $[x+(-7)][x+(-3)]=(x-7)(x-3)$
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