Chapter 8.7, Problem 4AGP

To determine

To factor: The given polynomial.

Answer to Problem 4AGP

The factored polynomial is $2x^2-32=2\left(x-4\right)\left(x+4\right)$ .

Explanation of Solution

Given information:

The given polynomial is $2x^2-32$ .

Concept used:

The difference of two squares can be factored as $a^2-b^2=\left(a-b\right)\left(a+b\right)$ .

Calculations:

The given polynomial P (say) is $E=2x^2-32$ .

  $\Rightarrow E=2\left(x^2-16\right)$

The polynomial $x^2-16$ can be written as the difference of two squares ${\left(x\right)}^2-{\left(4\right)}^2$ .

Therefore, the factored polynomial is $E=2\left(x^2-16\right)=2\left(x-4\right)\left(x+4\right)$

Conclusion:

The factored polynomial is $2x^2-32=2\left(x-4\right)\left(x+4\right)$ .