Factoring Polynomials| Algebra| ENGG10 LE1 Problem 9

SOLUTION:

$16x^4-200x^2+625$

Check criteria for perfect square trinomial.

$16x^4=\left(4x^2\right)^2$

$625=\left(25\right)^2$

$2\cdot \left(4x^2\right)\cdot \left(25\right)=200x^2$

Therefore, the given polynomial is a perfect square trinomial.

$=\left(4x^2-25\right)^2$

Now, $4x^2-25$ is a difference of two squares. So we have

$=\left[\left(2x-5\right)\left(2x+5\right)\right]^2$

The complete factored form of the given polynomial is

$=\left(2x-5\right)^2\left(2x+5\right)^2$