Understanding zeroes and factors of polynomials

Write the equation of the polynomial function
zeros: 0, -2, 4
degree: 5   
0 has a multiplicity of 3

• f(x) = x³(x-2)(x+4)
• f(x) = x³(x+2)(x-4)
• f(x) = x²(x-2)(x+4)
• f(x) = x²(x+2)(x-4)

Write a polynomial function of least degree for the given zeros:

• A

• B

• C

• D

• There are invisible zeros.

• There are no zeros.

• It has only one zero at (-6, 0).

• It has multiplicity (two zeros) at the point (-6, 0).

Write a quadratic function that has the following characteristics:

*negative leading coefficient

*bounces at x=7

• y = -(x + 7)

• y = -(x - 7)²

• y = -(x + 7)²

• y = -(x - 7)³

11) Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros:

 $9,\ -i$  

•  $f\left(x\right)=9x^3+9x^2-9x-9$  

•  $f\left(x\right)=x^3-9x^2+x-9$  

•  $f\left(x\right)=x^3+9x^2+9x-9$  

•  $f\left(x\right)=x^3+9x^2+x+9$  

Find a polynomial function that has zeroes at
x=4, -4, and 0

• x³ - 16x
• x³ - 8x
• x³ + 16x
• x³ + 8x

A polynomial, f(x), has zeros only at x = 3 and x = 7. Destiny wants to see if the function is above or below the x-axis between the two zeros so she can graph f(x). How should Destiny proceed?

• Destiny should substitute x = 0 into f(x).

• Destiny should substitute x = 3 into f(x).

• Destiny should substitute x = 4 into f(x).

• Destiny should substitute x = 1,000,000 into f(x).

What could be the equation of the polynomial function shown in this graph?

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A polynomial has zeros at  $x=9,\ \ x=1,\ and\ x=-2$ , Which of the following could be the function to represent this polynomial.

•  $P\left(x\right)=x\left(x+9\right)\left(x+1\right)\left(x-2\right)$  

•  $P\left(x\right)=\left(-2x\right)\left(x\right)\left(9x\right)$  

•  $P\left(x\right)=\left(x+2\right)\left(x-1\right)\left(x-9\right)$  

•  $P\left(x\right)=\left(x+9\right)\left(x+1\right)\left(x-2\right)$  

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