Chapter 8.7, Problem 27PPS

To determine

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

Answer to Problem 27PPS

The factored polynomial is $a^2-{49}^2=\left(a-7\right)\left(a+7\right)$ .

Explanation of Solution

Given information:

The given polynomial is $a^2-49$ .

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 $E=a^2-49$ that can be written as

  $\Rightarrow E={\left(a\right)}^2-{\left(7\right)}^2$

  $\Rightarrow E=\left(a-7\right)\left(a+7\right)$  Difference of two squares

Thus, the factored polynomial is $a^2-{49}^2=\left(a-7\right)\left(a+7\right)$ .

The, given polynomial is not a prime polynomial.

Conclusion:

The factored polynomial is $a^2-{49}^2=\left(a-7\right)\left(a+7\right)$ .