Chapter 6: Q. 126E (page 590)

In the following exercises, factor using the ‘ac’ method $30 x^{2} + 105 x - 60$

Short Answer

Expert verified

The factors are $15 (2 x - 1) (x + 4)$

Step by step solution

Step 1. Given Information

The trinomial is $30 x^{2} + 105 x - 60$

Find the factor using 'ac' method.

Step 2. Find GCF

Find GCF and factor it

GCF is 15

S0, $15 (2 x^{2} + 7 x - 4)$

Step 3. Find 'ac'

Compare the trinomial inside the parenthesis with $a x^{2} + b x + c$

So, $a = 2, b = 7, c = - 4$

so, $a c = - 8$

Find two number such as their product is role="math" localid="1644581551461" $a c = - 8$ and their addition is $b = 7$

So the numbers are 8 and -1.

Step 4. Split the middle and factor trinomial by grouping

Split the middle term

$15 (2 x^{2} + 8 x - x - 4)$

Factor it by grouping

$15 (2 x (x + 4) - 1 (x + 4))$

$15 (x + 4) (2 x - 1)$

Step 5. Check

To check multiply all factors, $15 (2 x - 1) (x + 4)$

$15 (2 x^{2} + 7 x - 4) 30 x^{2} + 105 x - 60$

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In the following exercises, factor using the ‘ac’ method $30 x^{2} + 105 x - 60$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find GCF

Step 3. Find 'ac'

Step 4. Split the middle and factor trinomial by grouping

Step 5. Check

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In the following exercises, factor using the ‘ac’ method30x2+105x−60

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find GCF

Step 3. Find 'ac'

Step 4. Split the middle and factor trinomial by grouping

Step 5. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, factor using the ‘ac’ method $30 x^{2} + 105 x - 60$