Question

Determine if the binomial is a perfect square binomial. If so, show the original monomial squared.

5. x2+ 16
6. x4 + 12x2+ 36

Answer 1

Explanation:

(5) x^2 + 16 is a perfect square binomial only if imaginary roots are allowed.

x^2 + 16 = (x + 4i)(x - 4i)

(6) x^4 + 12x^2 + 36 is a perfect square trinomial.

The square root of x^4 is x^2 and the square root of 36 is 6.

Experimenting, we find that x^4 + 12x^2 + 36 = (x² + 6)²

so we can conclude that x^4 + 12x^2 + 36 = (x² + 6)(x² + 6) = (x² + 6)².