Question

Which statement describes the graph of this polynomial function?

Answer 1

Answer:

Option (3)

Step-by-step explanation:

Given function is,

f(x) = x⁴ + x³ - 2x²

     = x²(x² + x - 2)

     = x²(x² + 2x - x - 2)

     = x²[x(x + 2) - 1(x + 2)]

     = x²(x + 2)(x - 1)

So the factored form of the polynomial function is,

f(x) = x²(x + 2)(x - 1)

For x - intercepts,

F(x) = x²(x + 2)(x - 1) = 0

x = -2, 1

This function has even multiplicity = 2 at x = 0.

Therefore, graph of the function will touch the x-axis at x = 0

And at other roots x = -2, 1 has odd multiplicity = 1, so the graph will cross the x-axis.

Option (3) will be the correct option.