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4.4

Factoring Trinomials of the Form ax 2 + bx + c by Grouping. 4.4. Factoring by Grouping. An alternative method that can be used to factor trinomials of the form ax 2 + bx + c, a ≠ 1 is called the grouping method . This method uses factoring by grouping. Example.

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4.4

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  1. Factoring Trinomials of the Form ax2 + bx + c by Grouping 4.4

  2. Factoring by Grouping An alternative method that can be used to factor trinomials of the form ax2 + bx + c, a ≠ 1 is called the grouping method. This method uses factoring by grouping. Example • Factor xy + y + 2x + 2 by grouping. Notice that, although 1 is the GCF for all four terms of the polynomial, the first 2 terms have a GCF of y and the last 2 terms have a GCF of 2. xy + y + 2x + 2 = x·y + 1 ·y + 2·x + 2· 1 = y(x + 1)+ 2(x + 1)= (x + 1)(y + 2)

  3. Factoring by Grouping To Factor Trinomials by Grouping Step 1: Factor out a greatest common factor, if there is one other than 1. Step 2: For the resulting trinomial ax2 + bx + c, find two numbers whose product is a • c and whose sum is b. Step 3: Write the middle term, bx, using the factors found in Step 2. Step 4: Factor by grouping.

  4. Factoring by Grouping Example Factor each of the following polynomials by grouping. • x3 + 4x + x2 + 4 = x ·x2 + x· 4 + 1· x2 + 1· 4 = x(x2 + 4) + 1(x2 + 4) = (x2 + 4)(x + 1) • 2x3 – x2 – 10x + 5 = x2 · 2x – x2· 1 – 5· 2x – 5· (– 1) = x2(2x – 1) – 5(2x – 1) = (2x – 1)(x2 – 5)

  5. Factoring by Grouping Example Factor 2x – 9y + 18 – xy by grouping. Neither pair has a common factor (other than 1). So, rearrange the order of the factors. 2x + 18 – 9y – xy = 2 · x + 2· 9 – 9 · y – x· y = 2(x + 9) – y(9 + x) = 2(x + 9) – y(x + 9)Make sure the factors are identical. = (x + 9)(2 – y)

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