Chapter 8.7, Problem 16CYU

To determine

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

Answer to Problem 16CYU

The factored polynomial is $3f^2-24f+48=3\left(f-4\right)\left(f-4\right)$ .

Explanation of Solution

Given information:

The given polynomial is $3f^2-24f+48$ .

Formula used:

The polynomial $a^2-2ab+b^2={\left(a-b\right)}^2=\left(a-b\right)\left(a-b\right)$ .

Calculations:

The given polynomial E (say) is $E=3f^2-24f+48$ that can be written as

  $\Rightarrow E=3\left(f^2-8f+16\right)$

  $\Rightarrow E=3\left(f^2-2\cdot f\cdot 4+4^2\right)$

  $\Rightarrow E=3{\left(f-4\right)}^2$    ${\left(a-b\right)}^2=a^2-2ab+b^2$

  $\Rightarrow E=3\left(f-4\right)\left(f-4\right)$

Thus, the factored polynomial is $3f^2-24f+48=3\left(f-4\right)\left(f-4\right)$ .

Given polynomial is not a prime polynomial.

Conclusion:

The factored polynomial is $3f^2-24f+48=3\left(f-4\right)\left(f-4\right)$ .