Question

Factor to find all x-intercepts of the function.
f, of, x, equals, minus, 4, x, to the power 4 , plus, 2, x, cubed, plus, 12, x, squared
f(x)=−4x
4
+2x
3
+12x
2

Answer 1

Factor out common terms:
f(x) = −4x^4 + 2x^3 + 12x^2 = −2x^2(2x^2 − x − 6)
Factor the quadratic:
2x^2 − x − 6 = (2x + 3)(x − 2)

So f(x) = −2x^2(2x + 3)(x − 2).

Set f(x)=0 → x = 0 (double root), x = −3/2, x = 2.

x-intercepts: (0, 0), (−3/2, 0), (2, 0).