Q. 370 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. 370 (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.
$6 p^{2} - 19 p q + 10 q^{2}$

Short Answer

Expert verified

By factoring the polynomial $6 p^{2} - 19 p q + 10 q^{2}$ completely by trial and error method, the factors are $(3 p - 2 q) (2 p - 5 q)$

Step by step solution

Step 1. Given

The polynomial is $6 p^{2} - 19 p q + 10 q^{2}$

To factor the polynomial by trial and error method.

Step 2. Factor any GCF

Factor the GCF.

There is no GCF in the polynomial.

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

The factors of the first term are $1, 6$ and $2, 3$

$6 p^{2} - 19 p q + 10 q^{2} = (6 p q) (p q)$

$6 p^{2} - 19 p q + 10 q^{2} = (p q) (6 p q)$

$6 p^{2} - 19 p q + 10 q^{2} = (2 p q) (3 p q)$

$6 p^{2} - 19 p q + 10 q^{2} = (3 p q) (2 p q)$

Step 4. Find all the factor pairs of third term

Consider the sign.

Since the last term is $10$ , the factors have same sign either positive or negative.

Since the sign of the second term is negative, both the factors have negative sign.

The factors of $10$ are

$- 1, - 10$
$- 2, - 5$

Step 5. Test all combination of factors

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

Possible outcomes	Product
$(6 p - 10 q) (p - q)$	$6 p^{2} - 16 p q + 10 q^{2}$
$(6 p - q) (p - 10 q)$	$6 p^{2} - 61 p q + 10 q^{2}$
$(3 p - 10 q) (2 p - q)$	$6 p^{2} - 23 p q + 10 q^{2}$
$(3 p - q) (2 p - 10 q)$	$6 p^{2} - 32 p q + 10 q^{2}$
$(6 p - 5 q) (p - 2 q)$	$6 p^{2} - 17 p q + 10 q^{2}$
$(6 p - 2 q) (p - 5 q)$	$6 p^{2} - 32 p q + 10 q^{2}$
$(3 p - 2 q) (2 p - 5 q)$	$6 p^{2} - 19 p q + 10 q^{2}$
$(3 p - q) (2 p - 10 q)$	$6 p^{2} - 32 p q + 10 q^{2}$

The factors of the trinomial is $(3 p - 2 q) (2 p - 5 q)$

Step 6. Check the answer

Check by multiplying the factor. $(3 p - 2 q) (2 p - 5 q) = 6 p^{2} - 15 p q - 4 p q + 10 q^{2}$

$= 6 p^{2} - 19 p q + 10 q^{2}$

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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.
$6 p^{2} - 19 p q + 10 q^{2}$

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.6p2-19pq+10q2

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

Decision Maths

Probability and Statistics

Geometry

Applied Mathematics

Calculus

Pure Maths

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.
$6 p^{2} - 19 p q + 10 q^{2}$