Section 3.2 Homework Questions?

Section

Concepts

3.2 Factoring Trinomials of the Form x2 + bx + c

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1. Factoring Trinomials with a Leading Coefficient of 1

Section 3.2 Factoring Trinomials of the Form x2 + bx + c

1. Factoring Trinomials with a Leading Coefficient of 1

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Consider the quadratic trinomialTo produce a leading term of we can construct binomials of the formThe remaining terms can be obtained from two integers, p and q, whose product is c and whose sum is b.

Example 1 Factoring a Trinomial of the Form x2 + bx + c

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Factor:Solution

The product of the first terms in thebinomials must equal the leading term of the trinomial. We must fillin 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 2 Factoring a Trinomial of the Form x2 + bx + c

Factor:Find two integers whose product is 50and 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 x2 + bx + c

1. Factoring Trinomials with a Leading Coefficient of 1

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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.

•

PROCEDURE Sign Rules for Factoring Trinomials

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Given the trinomial x2 + bx + c, the signs within thebinomial 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.

PROCEDURE Sign Rules for Factoring Trinomials

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Case 2 If c is negative, then the signs in the binomials must be different.

Example 3 Factoring Trinomials

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Factor. a. b.2 11 24x x 2 9 20t t

ExampleSolution:

4 Factoring Trinomials

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a. b.2 19 48y y

2 9 18x x 2 19 48x x

ExampleSolution:

5 Factoring Trinomials

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a. b.2 19 48y y

2 9 36x x 2 12x x

ExampleSolution:

6 Factoring Trinomials

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a. b.2 19 48y y

2 7 30x x 2 2 48x x

Example 7 Factoring Trinomials

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Factor. a. b.

ExampleSolution:

8 Factoring Trinomials

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a. b.

Section 3.2 Factoring Trinomials of the Form x2 + bx + c

1. Factoring Trinomials with a Leading Coefficient of 1

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To factor a trinomial of the form we must findtwo integers whose product is c and whose sum is b. If no such integers exist, then the trinomial is prime.

ExampleSolution:

5 Factoring Trinomials

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The trinomial is in descending order. The GCF is 1.

Find two integers whose product is 8 and whose sumis No such integers exist.

The trinomial is prime.

Section 3.2 Factoring Trinomials of the Form x2 + bx + cYou Try

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Factor completely2 7 10x x 2 11 18x x a. b.

Section 3.2 Factoring Trinomials of the Form x2 + bx + cYou Try

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Factor completely

a. b. 2 6 40x x 2 13 40x x

Section 3.2 Factoring Trinomials of the Form x2 + bx + cYou Try

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Factor completely

a. b. 216 10x x 25 20 15x x