Module 6 Review

Vocabulary Examples

Polynomial

Coefficient

x-intercept

factoring

polynomial function

-factored form

Roots/zeros

Practice

1. Distribute and show all work.

a.) 2y(x – 2) b.) (x – 2)(x + 1) c.) (2x – 4)(x + 3) d.) (x+ 4)² - 9

2. Factor the following binomials

a.) 4x + 24 b.) 16y – 12x c.) 3y² + 11y⁴ d.) 12x + 15y – 30t

Factor (cont.)

e.) x² + 12x + 27 f.) x² - 4x -12 g.) x² + 3x – 10 h.) 2x² + 8x + 6

3. When finding a root of a polynomial, we are trying to find the x- intercept (the place where y = 0. Set each of the following equations equal to zero and solve for x.

a. ) y = ( 2x + 4) b. y = ( x – 9) c. y = (3x + 5) d.) y = (x + 2)(x – 6)

4. Factor and find the roots for each polynomial.

a. ) f(x) = x² + 5x + 6 b.) f(x) = - x² - 4x - 3

5. Using the graphs provided, determine the equation of each of the polynomials in factored form.

6. Take the polynomial from standard form to factored form and graph the quadratic using the roots and y intercept (hint: the y-intercept comes from standard form)

a.) f(x) = x² + 7x + 10 b.) f(x) = x² - 15x + 36

c. How could we use the graph to find the vertex? What is the vertex for each graph?