Q. 371 Factor Trinomials of the Form ax... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 371 (page 635)

Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error
In the following exercises, factor completely using trial and error.
$- 9 a^{2} + 153 a + 18$

Short Answer

Expert verified

By factoring the polynomial $- 81 a^{2} + 153 a + 18$ completely by trial and error method, the factors are $- 9 (9 a + 1) (a - 2)$

Step by step solution

Step 1. Given

The polynomial is $- 81 a^{2} + 153 a + 18$

To factor the polynomial by trial and error method.

Step 2. Factor any GCF

Factor the GCF
$- 81 a^{2} + 153 a + 18 = - 9 (9 a^{2} - 19 a - 2)$

Step 3. Find all the pairs of factors of first term

The factors of the first term are $1, 9$ and $3, 3$

$9 a^{2} - 19 a - 2 = (x) (9 x)$

$9 a^{2} - 19 a - 2 = (3 x) (3 x)$

Step 4. Find all the factor pairs of third term

Consider the sign.

Since the last term is $- 2$ , the factors have opposite sign.

Since the sign of the second term is negative, the greater factor have negative sign.

The factors of $- 2$ are

$1, - 2$

Step 5. Test all combination of factors

Test all combination of factors until the correct product is found.

Possible factors	Product
$(9 a - 2) (a + 1)$	$9 a^{2} + 7 a - 2$
$(9 a + 1) (a - 2)$	$9 a^{2} - 17 a - 2$
$(3 a - 2) (3 a + 1)$	$9 a^{2} - 3 a - 2$
$(3 a + 1) (3 a - 2)$	$9 a^{2} + 3 a - 2$

The factors are $(9 a + 1) (a - 2)$

Step 6. Check the answer

Check by multiplying the factor.

$- 9 (9 a + 1) (a - 2) = - 9 (9 a^{2} - 18 a + a - 2)$

$= - 9 a (9 a^{2} - 17 a - 2)$

$= - 81 a^{2} + 153 a + 18$

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91影视

Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error
In the following exercises, factor completely using trial and error.
$- 9 a^{2} + 153 a + 18$

Short Answer

Step by step solution

Step 1. Given

Step 2. Factor any GCF

Step 3. Find all the pairs of factors of first term

Step 4. Find all the factor pairs of third term

Step 5. Test all combination of factors

Step 6. Check the answer

One App. One Place for Learning.

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91影视

Factor Trinomials of the Form ax2+bx+cUsing Trial and ErrorIn the following exercises, factor completely using trial and error.-9a2+153a+18

Short Answer

Step by step solution

Step 1. Given

Step 2. Factor any GCF

Step 3. Find all the pairs of factors of first term

Step 4. Find all the factor pairs of third term

Step 5. Test all combination of factors

Step 6. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error
In the following exercises, factor completely using trial and error.
$- 9 a^{2} + 153 a + 18$