Section 3.2 Homework Questions?

Section Concepts 3.2 Factoring Trinomials of the Form x 2 + bx + c Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Factoring Trinomials with a Leading Coefficient of 1

Section 3.2 Factoring Trinomials of the Form x 2 + bx + c 1.Factoring Trinomials with a Leading Coefficient of 1 Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Consider the quadratic trinomial To produce a leading term of we can construct binomials of the form The remaining terms can be obtained from two integers, p and q, whose product is c and whose sum is b.

Example 1Factoring a Trinomial of the Form x 2 + bx + c Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor: Solution The product of the first terms in the binomials must equal the leading term of the trinomial. We must fill in the blanks with two factors whose product is -45 and whose sum is 4. The factors will have unlike signs to produce a negative product (-45).

Example 2Factoring a Trinomial of the Form x 2 + bx + c Factor: Find two integers whose product is 50 and whose sum is -15. To form a positive product the factors must be either both positive or both negative. The sum must be negative, so we will choose negative factors of 50.

Section 3.2 Factoring Trinomials of the Form x 2 + bx + c 1.Factoring Trinomials with a Leading Coefficient of 1 Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Keep these important guidelines in mind: To factor a trinomial, write the trinomial in descending order such as For all factoring problems, always factor out the GCF from all terms first. Remember to factor out the opposite of the GCF when the leading coefficient of the polynomial is negative.

PROCEDURESign Rules for Factoring Trinomials Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Given the trinomial x 2 + bx + c, the signs within the binomial factors are determined as follows: Case 1 If c is positive, then the signs in the binomials must be the same (either both positive or both negative). The correct choice is determined by the middle term. If the middle term is positive, then both signs must be positive. If the middle term is negative, then both signs must be negative.

PROCEDURESign Rules for Factoring Trinomials Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Case 2 If c is negative, then the signs in the binomials must be different.

Example 3Factoring Trinomials Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor.a. b.

Example Solution: 4Factoring Trinomials Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. b.

Example Solution: 5Factoring Trinomials Slide 11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. b.

Example Solution: 6Factoring Trinomials Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. b.

Example 7Factoring Trinomials Slide 13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor.a. b.

Example Solution: 8Factoring Trinomials Slide 14 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a.b.

Section 3.2 Factoring Trinomials of the Form x 2 + bx + c 1.Factoring Trinomials with a Leading Coefficient of 1 Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. To factor a trinomial of the formwe must find two integers whose product is c and whose sum is b. If no such integers exist, then the trinomial is prime.

Example Solution: 5Factoring Trinomials Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The trinomial is in descending order. The GCF is 1. Find two integers whose product is 8 and whose sum is No such integers exist. The trinomial is prime.

Section 3.2 Factoring Trinomials of the Form x 2 + bx + c You Try Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor completely a.b.

Section 3.2 Factoring Trinomials of the Form x 2 + bx + c You Try Slide 18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor completely a.b.

Section 3.2 Factoring Trinomials of the Form x 2 + bx + c You Try Slide 19 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor completely a.b.