Chapter 8.6, Problem 4AGP

To determine

To factor: The polynomial $5x^2+13x+6$

Answer to Problem 4AGP

  $\left(x+2\right)\left(5x+3\right)$

Explanation of Solution

Given:

  $5x^2+13x+6$

Calculation:

The given polynomial is $5x^2+13x+6$

Rewrite the middle term as $13x=10x+3x$ . So, the polynomial becomes

  $5x^2+10x+3x+6$

Make group as shown below

  $\left(5x^2+10x\right)+\left(3x+6\right)$

Factor out the GCF from each of the group

  $5x\left(x+2\right)+3\left(x+2\right)$

Finally, factored out the common factor

  $\left(x+2\right)\left(5x+3\right)$

Therefore, the factored form of the given polynomial is $\left(x+2\right)\left(5x+3\right)$