Exploring Polynomials and Multiplicity

What could be the function for this graph in factored form?

• f(x) = (x-4)²(x+2)

• f(x) = (x+4)²(x-2)

• f(x) = (x-4)(x+2)²

• f(x) = (x+4)(x-2)²

f(x) = (x+2)(x-3)²(x-4) Which choice best describes the zeros?

• -2, 3 (multiplicity 2), 4

• -2 (multiplicity 2), 3, 4

• 2, -3 (multiplicity 2), -4

• 2 (multiplicity 2), -3, -4

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

If there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None

How many zeros does the polynomial function
 P(x) = 3x⁴+4x-8 have?

• 1

• 2

• 3

• 4

Determine the y-intercept
f(x) = x³- 5x²- 25x + 125

• (0,0)

• (0,25)

• (0,125)

• (0,5)

Which polynomial has this type of end behavior?

What is another way to say "where a function crosses the x-axis"?

• x-intercept

• zero

• root

• all of these.

The degree of the polynomial determines the max number of roots.

• True

• False

Factor
x² -16x + 48

• (x - 12)(x - 4)

• (x + 6)(x - 8)

• (x + 12)(x - 4)

• (x -16)(x - 3)