Multiplying and Factoring Polynomials

Write each equation in a form that makes the requested features easy to find. Show the new form of the equation and the features in your scrap paper. Do not use Desmos.

1.      y = x² + 4x + 4

            Find the following.

a.        Vertex:

            b.         Line of symmetry:

• a.        Vertex: x = -2

              b.         Line of symmetry: (-2, 0)

• a.        Vertex: (0, -2)

              b.         Line of symmetry: x = -2

• a.        Vertex: (-2, 0)

              b.         Line of symmetry: x = -2

• a.        Vertex: (2, 0)

              b.         Line of symmetry: x = 2

Factor y = x² + 5x - 24 and find give the following.      

          

a.        Factors

      b.   x -intercepts:

         c.        y  -intercept:

• a.        Factors: y = (x - 8) (x + 3)

        b.   x -intercepts: (8, 0) and (-3, 0)

           c.        y  -intercept: (0, -24)

• a.        Factors: y = (x + 8) (x - 3)

        b.   x -intercepts: (-8, 0) and (3, 0)

           c.        y  -intercept: (0, -24)

• a.        Factors: y = (x + 8) (x - 3)

        b.   x -intercepts: (0, -8) and (0, 3)

           c.        y  -intercept: (0, -24)

• a.        Factors: y = (x - 8) (x + 3)

        b.   x -intercepts: (-8, 0) and (3, 0)

           c.        y  -intercept: (0, 24)

Find the product.

(6k - 4) (4k - 5). Show your work on your scrap paper.

• 24k² − 46k + 20

• -24k² + 46k + 20

• 24k² + 46k + 20

• -24k² − 46k - 20

Multiply:

(3x + 3y) (8x² - 2xy + 8y²)

• 24x³ + 36x²y + 24y³

• 24x³ + 18x²y² + 18xy² + 24y²

• 24x³ - 18x²y + 18xy² - 24y³

• 24x³ + 18x²y + 18xy² + 24y³

Factor: x² - 5x - 36

• (x + 9) (x - 4)

• (x - 9) (x + 4)

• (x - 6) (x + 6)

• (x - 9) (x - 4)

Factor: 5r² - 46r - 40.

• (5r - 4) (r + 10)

• (5r + 4) (r − 10)

• (5r + 10) (r − 4)

• (r + 4) (5r − 10)

Factor: v² - 14v + 40.

• (v + 4) (v + 10)

• (v + 4) (v − 10)

• (v − 8) (v − 5)

• (v − 4) (v − 10)

Factor: b² - 16.

• (b + 2) (b - 8)

• (b + 8) (b - 2)

• (b - 4) (b + 4)

• (b - 4)(b - 4)

Express the volume (V) of a cube whose side is represented by 3x cm.

• V = 9x³ cm³

• V = 27x³ cm³

• V = 3x³ cm³

• V = 9x² cm³

A rectangular prism has dimensions x, x + 3, and 2x + 5. Determine the volume of the prism, in terms of x, in simplest form.

• V = 4x + 8

• V = 2x³ + 11x² + 15x

• V = x³ + 11x² + 15x

• V = 2x³ + 5x² + 6x +15