Factor Trinomials When the Coefficient of the Second-Degree Term is 1 (Objective #1)
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1 Factoring Trinomials (5.2) Factor Trinomials When the Coefficient of the Second-Degree Term is 1 EXAMPLE #1: Factor the trinomials. = = Factor Trinomials When the Coefficient of the Second-Degree Term is NOT 1 EXAMPLE #2: Factor the trinomials. Cross multiply the factors of a and c until the sum is equals b. Reverse the order before using a different set of factors. Write the factors of a and c in same order inside the parenthesis. 3a 2 8a + 5
2 Factoring multivariable Trinomials and Trinomials with GCF (Objective #3) Factoring multivariable trinomials: Apply Objective #1 or #2 depending on the leading coefficient. There should be exactly half of each variable in the middle. Factor the trinomial as ax 2 + bx + c but add the extra varaible on ends of each parenthesis as follows: EXAMPLE #3: Trinomails with GCF: EXAMPLE #4: Factor by Substitution (Objective #4) EXAMPLE #5: Factor by substitution.
3 5.2 Factoring Trinomials Factor Trinomial with leading coefficient of 1. Factor Trinomial with leading coefficient of 1. Factor Trinomial with leading coefficient NOT 1. Factor Trinomial with leading coefficient NOT 1. (Objective #3) Factor Multivariable Trinomial. (Objective #4) Factor by Substitution.
4 Rational Expressions and Functions; Multiplying and Dividing (6.1) Define rational expressions EXAMPLE #1: Which of the following is a rational expressions? (a) Write rational expressions in lowest terms (b) (c) Figure #1: EXAMPLE #2: Reduce to lowest terms. (a) (b) (c)
5 Multiply rational expressions (Objective #3) EXAMPLE #3: Multiply. Figure #2: Find reciprocals of rational expressions (Objective #4) EXAMPLE #4: Find the reciprocal. Divide rational expressions (Objective #5) EXAMPLE #5: Divide. Figure #3:
6 6.1 Rational Expressions and Functions; Multiplying and Dividing Which of the following is a rational expression? Reduce to lowest terms. (a) (b) (c) (Objective #3) Multiply. (Objective #3) Multiply. (Objective #4) Find the reciprocal. (Objective #5) Divide.
7 Special Factoring (5.3) Factor a difference of squares To factor a difference of squares first rewrite each term as a square then use the following formula: EXAMPLE #1: Factor a perfect square trinomial To factor a perfect square trinomial first rewrite the first and last term as squares, check to see if the middle is twice the base of the first and last term, and then use the following formula: EXAMPLE #2: =
8 Factor a difference of cubes (Objective #3) To factor a difference of cubes first rewrite each term as a cube then use the following formula: EXAMPLE #3: Factor a sum of cubes (Objective #4) To factor a sum of cubes first rewrite each term as a cube then use the following formula: EXAMPLE #4:
9 5.3 Special Factoring Factor a difference of squares. Factor a difference of squares. Factor a perfect square trinomial. Factor a perfect square trinomial. (Objective #3) Factor a difference of cubes. (Objective #4) Factor a sum of cubes.
10 Greatest Common Factor and Factor by Grouping (5.1) Identifying the Greatest Common Factor The greatest common factor (GCF) of two or more terms is the largest factor that is common to each term. To find the greatest common factor break down each term as much as possible (prime factors) as follows: EXAMPLE #1: Identify the GCF. Figure 1 Figure 2 Factoring Out the Greatest Common Factor Identify the greatest common factor, write the GCF outside the parenthesis, and then write the remaining factors inside the parenthesis as follows: EXAMPLE #2: Factor out the GCF. Figure 3 Figure 4 Factoring Out a Negative Factor (Objective #3) Factor out a negative common factor if the first term has a negative coefficient (leading coefficient) as follows: EXAMPLE #3: Factor out a negative GCF. a) Figure 5
11 Factoring out a binomial Factor (Objective #4) Binomial factors have two terms inside of a parenthesis and is common in each term. Factor out a common binomial factor as follows: EXAMPLE #4: Figure 6 Figure 7 Figure 8 Factor by Grouping (Objective #5) Use factor by grouping if the polynomial has 4 or more terms. Split the polynomial into two groups and factor out a GCF in each group. If there is 4 terms in the polynomial there should be a common binomial factor if not, factor by grouping does not apply. If there is a common binomial factor then factor it out as follows: EXAMPLE #5: Factor by Grouping. a) b) Figure 9
12 5.1 Greatest Common Factor and Factor by Grouping Identify the greatest common factor. Factor out the greatest common factor. (Objective #3) Factor out a negative common factor. (Objective #4) Factor out a common binomial factor. (Objective #5) Factor by grouping. (Objective #5) Factor by grouping.
13 Solving Equations by the Zero-Factor Property (5.5) Learn and Use the Zero-Factor Property How to use the zero-factor property to solve equations: EXAMPLE #1: EXAMPLE #2: Solve Applied Problems that Require the Zero-Factor Property
14 5.5 Solving Equations by Zero-Factor Property Solve quadratic equation. Solve quadratic equation. Solve quadratic equation. Solve quadratic equation. Apply quadratic equations. Apply quadratic equations.
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