Chapter 8.6, Problem 4BGP

To determine

To factor: The polynomial $6x^2+22x-8$

Answer to Problem 4BGP

  $2\left(x+4\right)\left(3x-1\right)$

Explanation of Solution

Given:

  $6x^2+22x-8$

Calculation:

The given polynomial is $6x^2+22x-8$

Rewrite the middle term as $22x=24x-2x$ . So, the polynomial becomes

  $6x^2+24x-2x-8$

Make group as shown below

  $\left(6x^2+24x\right)+\left(-2x-8\right)$

Factor out the GCF from each of the group

  $6x\left(x+4\right)-2\left(x+4\right)$

Finally, factored out the common factor

  $\left(x+4\right)\left(6x-2\right)$

This can be further simplified by factor out GCF 2 from $\left(6x-2\right)$

  $2\left(x+4\right)\left(3x-1\right)$

Therefore, the factored form of the given polynomial is $2\left(x+4\right)\left(3x-1\right)$