Answer quickly which statement describes the graph of this polynomial function f(x) = x^4 + x^3 -2x^2

The correct answer is C.

You can tell this by factoring the equation to get the zeros. To start, pull out the greatest common factor.

f(x) = x^4 + x^3 - 2x^2

Since each term has at least x^2, we can factor it out.

f(x) = x^2(x^2 + x - 2)

Now we can factor the inside by looking for factors of the constant, which is 2, that add up to the coefficient of x. 2 and -1 both add up to 1 and multiply to -2. So, we place these two numbers in parenthesis with an x.

f(x) = x^2(x + 2)(x - 1)

Now we can also separate the x^2 into 2 x's.

f(x) = (x)(x)(x + 2)(x - 1)

To find the zeros, we need to set them all equal to 0

x = 0

x = 0

x + 2 = 0

x = -2

x - 1 = 0

x = 1

Since there are two 0's, we know the graph just touches there. Since there are 1 of the other two numbers, we know that it crosses there.