Which statement describes the graph of this polynomial function?

f (x) = x4 + x3 - 2x

The graph crosses the x-axis at x = 2 and x = - 1 and touches the x-axis at x = 0.

The graph touches the x-axis at x = 2 and x = - 1 and crosses the x-axis at x = 0.

The graph crosses the x-axis at x = - 2 and x = 1 and touches the x-axis at x = 0.

O The graph touches the x-axis at x = - 2 and x = 1 and crosses the x-axis at x = 0.

Answer: C. The graph crosses the x-axis at x=-2 and x=1 & touches the x-axis at x=0

Step-by-step explanation:

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.