Question

Determine the x-intercepts for
y = x^3 + 4x^2 - 4x - 16

and for

y = 2x^4 - 5x^2

Answer 1

Factor the expression. The intercepts are all rational roots.

Since the constant term is 16, and the coefficient of x³ is +1, the only rational factors to try are powers of 2.
You will find one intercept in the negative x region, and two in the positive x region.

The trial roots can be tested rather simply by evaluation the expression
y = f(x) = x^3 + 4x^2 - 4x - 16
For x=2,
f(2) = 2&sup3 + 4(2)² -4(2) -16
= 16 + 8 - 8 - 16
=0
Therefore (x-2) is a factor, or x=+2 is an intercept.
Continue this way to find all the roots, or alternatively, reduce the expression by long division with (x-2).

Post your answer for a check if you wish.

For
y = 2x^4 - 5x^2
you can factor out the common factor x² to get
y=x²(2x&sup2-5)
from which you can figure out the intercepts.