Chapter 11.4, Problem 89S

To determine

To calculate: To factor the polynomial

Answer to Problem 89S

On factoring, the polynomial is $4\left(2x-5\right)\left(x+2\right)$

Explanation of Solution

Given information: Polynomial is $8x^2-4x-40$

Formula Used:

Polynomial can be factored using one of the following ways:

• Greatest Common Factor
• Grouping
• Difference in two squares
• Sum or difference in two cubes
• Trinomials

Calculation:

Polynomial is given as

  $8x^2-4x-40$

Taking out $2$ common,

  $4\left(2x^2-x-10\right)$

Factoring the above by grouping,

  $\begin{array}{l}4\left(2x^2+4x-5x-10\right)\\ 4\left(2x\left(x+2\right)-5\left(x+2\right)\right)\\ 4\left(\left(2x-5\right)\left(x+2\right)\right)\\ 4\left(2x-5\right)\left(x+2\right)\end{array}$

Conclusion:

Hence, polynomial on factoring is $4\left(2x-5\right)\left(x+2\right)$