Chapter 8.7, Problem 25PPS

To determine

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

Answer to Problem 25PPS

The factored polynomial is $12p^3-3p=3p\left(p-1\right)\left(p+1\right)$ .

Explanation of Solution

Given information:

The given polynomial is $12p^3-3p$ .

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 $E=12p^3-3p$ that can be written as

  $\Rightarrow E=3p\left(p^2-1\right)$

  $\Rightarrow E=3p\left({(p)}^2-{(1)}^2\right)$       Difference of two squares

  $\Rightarrow E=3p\left(p-1\right)\left(p+1\right)$

Thus, the factored polynomial is $12p^3-3p=3p\left(p-1\right)\left(p+1\right)$ .

The given polynomial is not a prime polynomial.

Conclusion:

The factored polynomial is $12p^3-3p=3p\left(p-1\right)\left(p+1\right)$ .