Algebra Review

Warm-up (3 m) Multiply: 1. 4x 2 (7x 3 - 6x x - 10) 2. (3x 2 - 5)(x + 4) Factor: 3. x 3 – 64x4. 9x 2 – 9x – 4

We’re going to review the following skills for the next unit: Multiplying Polynomials Factoring Polynomials Simplifying Rational Expressions Multiplying Rational Expressions Dividing Rational Expressions Adding and Subtracting Rational Expressions

Multiplying Polynomials Distribute Multiply each term inside the parentheses by the term outside the parentheses. 3x 5 (x 7 – 2x x) FOIL First – Outer – Inner – Last (3x + 5)(x – 7)

Multiplying Polynomials, cont. Works well when you multiply anything larger than a binomial and a binomial. – Example: (3x 2 – x + 1)(x 2 + 2x – 3) Very similar to long multiplication by hand. Vertical Multiplication

Example (7x 2 – 5x +6)(2x – 1)

Example (3x 2 – x + 1)(x 2 + 2x – 3)

Multiplying with Trigonometric Functions Exactly the same as multiplying without trigonometric functions.

Your Turn: Multiply problems 1 – 10 in the Algebra Review packet

Factoring Remember, there are four types of factoring that we reviewed at the beginning of the semester: – Leading Coefficient = 1 (“Regular” Factoring) – Leading Coefficient ≠ 1 (Box Method or Welsh Method) – Greatest Common Factor (GCF) – Difference of Squares

Leading Coefficient = 1 x 2 – 7x + 10

Leading Coefficient ≠ 1 3x 2 – 11x – 20

Greatest Common Factor 4x 4 – 40x 3 + 8x 2

Difference of Squares 81x 4 – 100

Factoring with Trigonometric Functions Exactly the same as factoring without trigonometric functions.

Your Turn: Factor problems 11 – 24 in the Algebra Review packet.

23.24.

Warm-up (3 m) 1. Multiply:2. Factor: Find the reciprocals of the numbers below:

Seek and Solve!!! Show all your work on a piece of paper. I’m collecting it for a classwork grade.

Simplifying Rational Expressions You can only cancel factors that are separated by multiplication!!! Wrong!!! Right!!!

Simplifying Rationals, cont. You can also reduce factors – as long as they’re separated by multiplication.

Simplifying Rationals, cont. 1.Factor the numerator and the denominator 2.Optional – Identify the factors in the numerator and the denominator. 3.Cancel common factors in the numerator and the denominator.

Example Factors in Numerator Factors in Denominator

Example Factors in Numerator Factors in Denominator

Example Factors in Numerator Factors in Denominator

Your Turn: Simplify problems 25 – 32 in the Algebra Review packet. Remember to factor the numerator and the denominator first, AND you can only cancel factors separated by multiplication.

Warm-up (3 m) 1.Simplify:

Homework Review

Multiplying Rational Expressions 1.Factor the numerator and the denominator. 2.Cancel and/or cross cancel any common factors that are separated by multiplication. 3.Optional – Rewrite the simplified fractions. 4.Multiply across. (Multiply the numerators together and the denominators together.)

Example

Your Turn Multiply problems 33 – 38 in the Algebra Review packet. Simplify your answers.

Warm-up (4 m) 1.Simplify: 2.Multiply:

What About…?

Dividing Rational Expressions Division is the same thing as multiplication by the reciprocal!

Dividing Rationals, cont. 1.Rewrite the division as multiplication by the reciprocal. 2.Factor the numerator and the denominator. 3.Cancel and/or cross cancel any common factors separated by multiplication. 4.Multiply across.

Example

Your Turn: Divide problems 39 – 48 in the Algebra Review packet.

Adding and Subtracting Rational Expressions If the fractions have the same denominator, add or subtract the numerators. (Make sure to distribute the subtraction sign!!!) Simplify the fraction is possible.

Examples

Adding and Subtracting Rational Expressions, cont. If the fractions have the different denominators, 1.Factor the numerator and the denominator. 2.Simplify each fraction individually if possible. 3.Compare the denominators of each fraction. Identify the “missing” factors from each fraction. (Finding the Least Common Denominator) 4.Multiply each fraction by 1. Rewrite 1 as

Adding and Subtracting Rational Expressions, cont. 5.Multiply across. 6.Combine all fractions into one fraction. 7.Simplify the numerator. 8.Factor the numerator if possible. 9.Simplify/reduce the fraction if possible.

Examples in Smart Board File

Example

Your Turn: Add or subtract problems 49 – 62 in the Algebra Review packet.

61.62.

Activity!!!