Factor and Solve Polynomial Equations

2.3 (GREEN book)

Polynomial Review WS: due TOMORROW

Vocabulary

A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients.

Vocabulary

To factor the sum of two cubes, use the pattern:

a3 + b3 = (a + b)(a2 – ab + b2)

To factor the difference of two cubes, use the pattern:

a3 – b3 = (a – b)(a2 + ab + b2)

Vocabulary

For some polynomials you can factor by grouping pairs of terms that have a common monomial factor.

Example 1:

Factor the polynomial completely

1. 4x4 – 108x

2. 2b3 + 16a3

Example 2:

Factor the polynomial x3 + 2x2 – x – 2 completely.

We need to factor

by grouping

Example 3:

Factor completely:

1. 3x8 + 18x5 + 24x2

2. 81g4 - 256

Example 4:

Find the real-number solutions of the equation x4 – 7x2 = -12

To Solve: write in

standard form and

then factor

Example 5.

The dimensions (in inches) of a jewelry box are: length 4x, width (x – 1), and height (x – 2). If the volume of the box is 24 cubic inches, find the dimensions of the box.

Homework:

P. 78 #1-25odd

Fix/Complete Polynomials Review WS (due tomorrow)