Chapter 8.7, Problem 1CYU

To determine

To find: That the given polynomial is a difference of squares, if yes then to factor it.

Answer to Problem 1CYU

The polynomial $q^2-121$ is a difference of two squares, so it can be factorized. The factored polynomial is $q^2-121=\left(q-11\right)\left(q+11\right)$ .

Explanation of Solution

Given information:

The given polynomial is $q^2-121$ .

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 $P=q^2-121$ .

The polynomial can be written as $P=q^2-{\left(11\right)}^2$ , i.e., difference of two squares.

The factors of polynomial P are

  $P=q^2-{\left(11\right)}^2$

  $\Rightarrow P=\left(q-11\right)\left(q+11\right)$

Thus, the given polynomial $q^2-121$ is a difference of two squares, so it can be factorized. The factored polynomial is $q^2-121=\left(q-11\right)\left(q+11\right)$ .

Conclusion:

The polynomial $q^2-121$ is a difference of two squares, so it can be factorized. The factored polynomial is $q^2-121=\left(q-11\right)\left(q+11\right)$ .