Chapter 8.7, Problem 22PPS

To determine

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

Answer to Problem 22PPS

The factored polynomial is $8c^2-88c+242=2\left(2c-11\right)\left(2c+11\right)$ .

Explanation of Solution

Given information:

The given polynomial is $8c^2-88c+242$ .

Concept used:

To factor expression $x^2-2xy+y^2={\left(x-y\right)}^2$ .

Calculations:

The given polynomial E (say) is $E=8c^2-88c+242$ that can be written as

  $\Rightarrow E=2\left(4c^2-44c+121\right)$

The polynomial $4c^2-44c+121$ may be written as

  $4c^2-44c+121={\left(2c\right)}^2-2\cdot 2c\cdot 11+{\left(11\right)}^2$

  $\Rightarrow 4c^2-44c+121={\left(2c-11\right)}^2$

  $\Rightarrow 4c^2-44c+121=\left(2c-11\right)\left(2c-11\right)$

Therefore, $E=2\left(2c-11\right)\left(2c+11\right)$

Thus, the factored polynomial is $8c^2-88c+242=2\left(2c-11\right)\left(2c+11\right)$ .

The given polynomial is not a prime polynomial.

Conclusion:

The factored polynomial is $8c^2-88c+242=2\left(2c-11\right)\left(2c+11\right)$ .