Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises: 2

Answer

To factor the trinomial $x^{2}$ + 7x + 10, we look for two integers whose product is 10 and whose sum is 7. These integers are 5 and 2, so the trinomial factors as (x + 5)(x + 2).

Work Step by Step

When factoring a trinomial of the form M$x^{2}$ + Nx + O, where M, N, and O are real numbers, the trinomial can be factored into two binomials of the form (Ax + B)(Cx + D), where A, B, C, and D are real numbers. If the $x^{2}$ term does not have a coefficient, then the two x terms (A and B) will have a coefficient of 1 and the constants (C and D) will be the factors of O that sum to N. In this case, we are looking for two terms whose product is 10 and whose sum is 7. The products of 10 are: 1, 2, 5, and 10, so the terms must either be 10 and 1 or 5 and 2. 5 and 2 adds to 7, therefore these are the constants.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.