Roots, Zeros and Intercepts of Polynomials

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

• f(x) = (x+2)(x-1)(x-4)

• f(x) =x³ - 3x² - 6x + 8

• f(x) = x³ + 8

• f(x) = x³ - 3x² + 8

The degree of a polynomial determines...

• the maximum number of x-intercepts

• the number of turning points

• if the end behavior is up or down

• the y-intercept

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.

• No, (x-2) is  not a factor. The remainder is zero.

• Yes, (x-2) is a factor. The remainder is zero.

• No, (x-2) is  not a factor. There is a remainder. 

Which of the following is a completely factored polynomial?

• f(x)=2x⁴-3x³+8x-6

• f(x)=x²(x-1)(x+3)

• f(x)=x(x²-16)

• f(x)=(2x+1)(x²-3x-18)

What are the roots of the polynomial?

• -3, 0, and 3

• 0

• -2, 10, and -10

• 11, 0 and -11

If a zero of a polynomial function has multiplicity 2 that means:

• The x intercept is at (2, 0)

• The graph will "bounce back" at that zero

• The graph will "pass through" at that zero

• Zeros cannot have multiplicity of 2

Which x-value is a root of the function below? f(x) = x³ + 4x² + 9x + 36

• x = 3

• x = -3

• x = 4

• x = -4

If f(x) = 2x³-13x²+36, is x = 6 an x-intercept?

• No, because f(6) = 30

• Yes, because f(6) = 0

• Yes, because f(6) = 30

• No, because f(6) = 0

• 2

• 1

• 3

• 0

• -3,2,1

• 3,-2,-1