Solving Polynomials Finding All Zeros

Factor the polynomial and find all zeros.

• A

• B

• C

• D

A polynomial function is shown below in factored form. f\left(x\right)=5\left(2x+3\right)\left(x+4\right)\left(x-2\right) Which of these statements are true? The function has exactly ​ zeros. The graph of the function has an x-intercept at ​ .

• 3

• (2, 0)

• 4

• 5

• 2

• (4, 0)

• (0, 0)

Factor the polynomial and find all zeros.

• A

• B

• C

• D

Explain the concept of multiplicity of roots in polynomial equations.

• Multiplicity of roots is the same as the degree of the polynomial equation

• Multiplicity of roots indicates the size of the roots in the solution set

• Multiplicity of roots in polynomial equations refers to the number of variables in the equation

• In polynomial equations, multiplicity of roots refers to the number of times a particular root appears in the solution set.

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

What is the equation of this graph in factored form?

• (x - 1)(x + 3)²

• (x - 1)²(x + 3)

• (x + 1)²(x - 3)

• (x + 1)(x - 3)²

What does multiplicity of a zero mean?

• Look at the number of terms

• How many times the zero repeats

• Find the sum of all the coefficients

• Ratio your x and y

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

• 5

• 4

• 3

• 2

Which is true about the equation of the graph shown?

• The function has an Odd degree

• The function has an Even degree

• The function has 5 real zeros

• The function has a positive leading coefficient