Chapter 8.7, Problem 20PPS

To determine

To factor: The given polynomial, if possible. If the polynomial cannot be factored, write prime.

Answer to Problem 20PPS

The factored polynomial is $16a^2-121b^2=\left(4a-11b\right)\left(4a+11b\right)$ .

Explanation of Solution

Given information:

The given polynomial is $16a^2-121b^2$ .

Formula used:

The factors of polynomial that is difference of two squares are $a^2-b^2=\left(a+b\right)\left(a-b\right)$ .

Calculations:

The given polynomial E (say) is $E=16a^2-121b^2$ that can be written as

  $\Rightarrow E={\left(4a\right)}^2-{\left(11b\right)}^2$

  $\Rightarrow E=\left(4a-11b\right)\left(4a+11b\right)$       Difference of two squares

Thus, the factored polynomial is $16a^2-121b^2=\left(4a-11b\right)\left(4a+11b\right)$ .

Given polynomial is not a prime polynomial.

Conclusion:

The factored polynomial is $16a^2-121b^2=\left(4a-11b\right)\left(4a+11b\right)$ .