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Which statement describes the graph of this polynomial function?
f(x)= x4+ x3 - 2x2
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.
O 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.

Which statement describes the graph of this polynomial function fx x4 x3 2x2 The graph crosses the xaxis at x 2 and x 1 and touches the xaxis at x 0 The graph t class=

Respuesta :

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.

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