Chapter 6: Q. 139E (page 590)

In the following exercises, factor each expression using any method. $12 y^{2} - 29 y + 14$

Short Answer

Expert verified

The factors are $(4 y - 7) (3 y - 2)$

Step by step solution

Step 1. Given Information

The trinomial is $12 y^{2} - 29 y + 14$

Find factors using 'ac' method

Step 2. Find 'ac'

Compare the trinomial to $a x^{2} + b x + c$ and find product 'ac'

$12 y^{2} - 29 y + 14$ So, $a = 12, b = - 29, c = 14$

Hence $a c = 168$

Find two numbers such as product is 168 and sum is $- 29$

So, the numbers are $- 21, - 8$

Step 3. Factor the trinomial

Split the middle term of trinomial to find factors

$12 y^{2} - 21 y - 8 y + 14$

Factor it

$3 y (4 y - 7) - 2 (4 y - 7) (4 y - 7) (3 y - 2)$

Step 4. Check

Multiply the factors $(4 y - 7) (3 y - 2)$

$12 y^{2} - 21 y - 8 y + 14 12 y^{2} - 29 y + 14$

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In the following exercises, factor each expression using any method. $12 y^{2} - 29 y + 14$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find 'ac'

Step 3. Factor the trinomial

Step 4. Check

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In the following exercises, factor each expression using any method.12y2−29y+14

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find 'ac'

Step 3. Factor the trinomial

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Decision Maths

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each expression using any method. $12 y^{2} - 29 y + 14$