Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Review Exercises: 90

Answer

$(x-4)(x-7)$

Work Step by Step

To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$. In the case of $x^2-11x+28$, we are looking for two numbers whose product is $28$ and whose sum is $-11$. The numbers $-7$ and $-4$ meet these criteria, because $$-4\times-7=28\;\text{and}\;-4+-7=-11.$$When we insert these numbers into the blanks, we arrive at the factors $(x-4)(x-7)$.
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