Polynomials Linear Factors and Zeros

• is the graph of
  y = x² - 2x + 4
• is the graph of
  y = -x² - 2x + 4

If the problem asks you to factor a polynomial knowing that (x - 5) is a factor, what number do you synthetically divide by?

• -5

• 5

Factor the polynomial.  One factor is (x - 5).
f\left(x\right)=2x^3-9x^2-11x+30

Find the polynomial that the degree of 4 and has zeros: x = 4i, 1, 2 

• (x+4i)(x-4i)(x-1)(x+2)

• (x-4i)²(x-1)(x+2)

• (x+4i)(x-4i)(x+1)(x-2)

• (x+4i)²(x+1)(x-2)

Mathematical Equivalence

ON

Write the factors of the polynomial from the zeros in the graph.
Remember to look at your roots, multiplicity, and end behavior!!
Use your notes!

• (x - 3) (x + 2) (x + 5)

• (x - 5) (x - 2) (x + 3)

• (x + 3) (x + 2) (x + 5)

• (x - 3) (x - 2) (x - 5)

Write the factors of the polynomial from the zeros in the graph. Remember to look at your roots, multiplicity, and end behavior!! Use your notes!

• (x - 3) (x + 2) (x + 5)

• (x - 5) (x - 2) (x + 3)

• (x + 3) (x + 2) (x + 5)

• (x - 3) (x - 2) (x - 5)

• There is no relationship between the factors and the zeros.

• If you set each factor equal to 0 and solved you would get the zeros.

• The number inside each parenthesis are the zeros of the equation

• The zero is the sum of the numbers inside the parenthesis.