Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Review - Exercises - Page 134: 35


$(4x^{2}$ + 3)(x - 2)

Work Step by Step

Since this is a cubic polynomial, we will not be able to factor it normally like a second degree polynomial. For cubic polynomials, you need to group the function into 2 separate groups of like factors and factor them. 1. So the first group I decided to use was $4x^{2}$ and 8$x^{2}$ since they both have a 4 and $x^{2}$ in common. 2. Factoring the group mentioned above, you get $4x^{2}$(x - 2). 3. For the second group, I used the last two terms 3x and -6. 4. These two terms have a 3 in common between them both. 5. Factoring the 3x and -6 mentioned above, we get 3(x - 2). 6. Combing our factored forms we get from both groups we get $4x^{2}$(x - 2) + 3(x - 2). 7. Now you have a common factored terms, (x-2). 8. The other factored group is the terms that are left. 9. So our final factored form is $(4x^{2}$ + 3)(x - 2).
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