Section 3.4 Homework Questions?

Section

Concepts

3.4 Factoring Trinomials: Trial-and-Error Method

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1. Factoring Trinomials by the Trial-and-Error Method

Section 3.4 Factoring Trinomials: Trial-and-Error Method

1. Factoring Trinomials by the Trial-and-Error Method

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The method presented in this section is called the trial-and-error method.We will factor quadratic trinomials of the form

Section

We need to fill in the blanks so that the product of the first terms in the binomials is 2x2

3.4 Factoring Trinomials: Trial-and-Error Method

1. Factoring Trinomials by the Trial-and-Error Method

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and the product of the lastterms in the binomials is 6. Furthermore, the factors of 2x2

and 6 must be chosen so that the sum of the products of the inner terms and outer terms equals 7x.

PROCEDURE Trial-and-Error Method to Factor ax2 + bx + c

(continued)

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Step 1 Factor out the GCF.Step 2 List all pairs of factors of a and pairs of factors of c. Consider the reverse order for one of the lists of factors.Step 3 Construct two binomials of the form:

Step 4 Test each combination of factors and signs until the sum of the products of the outer terms and inner terms gives the middle term.

Step 5 If no combination of factors produces the correct product, the trinomial cannot be factored further and is a prime polynomial

(x )(x )

PROCEDURE Sign Rules for the Trial-and-Error Method

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Given the trinomial ax2 + bx + c, (a > 0), the signs can be determined as follows:• 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 the Trial-and-Error Method

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• If c is negative, then the signs in the binomial must be different. The middle term in the trinomial determines which factor gets the positive sign and which gets the negative sign.

Section 3.4 Factoring Trinomials: Trial-and-Error Method

1. Factoring Trinomials by the Trial-and-Error Method

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Keep these two important guidelines in mind:

• For any factoring problem you encounter, always factor out the GCF from all terms first.

• To factor a trinomial, write the trinomial in the form ax2 + bx + c.

No binomial may contain a common factor•

Example 1 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial-and-error method:

Example 2 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial-and-error method:26 11 4x x

Example 3 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial-and-error method:210 11 3x x

Example 4 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial-and-error method:215 19 6x x

Example 5 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial-and-error method:22 27 14x x

Example 6 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial-and-error method:218 9 5x x

Example 7 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial and error method:

Example 8 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial-and-error method:

Example 9 Factoring a Trinomial by the Trial-and-Error Method

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Factor the trinomial by the trial and error method:

Avoiding Mistakes

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Do not forget to write the GCF in the final answer.

Section 3.4 Factoring Trinomials: Trial-and-Error MethodYou Try

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Factor the trinomial by the trial and error method23 19 6x x

Section 3.4 Factoring Trinomials: Trial-and-Error MethodYou Try

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Factor the trinomial by the trial and error method214 15 9x x

Section 3.4 Factoring Trinomials: Trial-and-Error MethodYou Try

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Factor the trinomial by the trial and error method3 29 12 4x y x y xy