1 5x 2 9x 4 2 6x 2 7x 3 3 4x 2 16xy 7y 2 18 533 Factoring Trinomials with a

# 1 5x 2 9x 4 2 6x 2 7x 3 3 4x 2 16xy 7y 2 18 533

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1. 5x 2 + 9x + 4 2. 6x 2 + 7x 3 3. 4x 2 16xy + 7y 2 18 5.3.3: Factoring Trinomials with a Common Factor The first step in any factoring process is to remove any existing common factors. It may be necessary to combine common-term factoring with other methods (such as factoring a trinomial into a product of binomials) to completely factor a polynomial. Examples: Factor the following trinomials. 1. 2x 2 16x + 30 2. 6x 3 + 15x 2 y 9xy 2 19 5.3.3: Completely Factor a Trinomial One final note: When factoring, we require that all coefficients be integers. Given this restriction, not all polynomials are factorable over the integers. Examples: Factor the following trinomials. 1. x 2 9x + 12 20 5.4: Factoring Trinomials: The ac Method Objectives: 5.4.1: Use the ac test to determine factorability. 5.4.2: Factor a trinomial using the ac method. 5.4.3: Completely factor a trinomial 21 5.4.1: Use the ac Test to Determine Factorability. Some students prefer the method of this section (called the ac method ) because it yields the answer in a systematic way . Not all trinomials can be factored. To discover whether a trinomial is factorable, we try the ac test. 22 5.4.1: Use the ac Test to Determine Factorability. Examples: Use the ac test to determine which of the following trinomials can be factored . Find the values of m and n for each trinomial that can be factored. 1. x 2 3x 18 2. x 2 24x + 23 3. x 2 11x + 8 4. 2x 2 + 7x 15 23 5.4.2: Factor a Trinomial Using the ac Method. Examples: Factor using the ac method 1. 2x 2 13x 7 2. 6x 2 5x 6 24 5.4.3: Completely Factor a Trinomial The first step in any factoring process is to remove any existing common factors. Examples: Factor the following trinomials. 1. 3x 2 12x 15 25 5.5: Strategies in Factoring Objectives: 5.5.1: Recognize factoring patterns. 5.5.2: Apply appropriate factoring strategies. 26 5.5.1: Recognize factoring patterns. 1. Always look for a greatest common factor. If you find a GCF (other than 1), factor out the GCF as your first step. 2. Now look at the number of terms in the polynomial you are trying to factor. A. If the polynomial is a binomial, consider the special binomial formulas.  #### You've reached the end of your free preview.

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• Fall '18
• jane
• Accounting, Quadratic equation, Elementary algebra
• • •  