Factoring Polynomials| Algebra| ENGG10 LE1 Problem 9

Factor the polynomials completely.

16x^4-200x^2+625

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

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