Q. 139E - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given Information

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

Find factors using 'ac' method

Step 2. Find 'ac'

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

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

Hence $ac=168$

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

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

Factor it

$$\begin{gathered} 3y\left(4y-7\right)-2\left(4y-7\right) \\ \left(4y-7\right)\left(3y-2\right) \end{gathered}$$

Step 4. Check

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

$$\begin{gathered} 12y^2-21y-8y+14 \\ 12y^2-29y+14 \end{gathered}$$