Factoring.

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Presentation transcript:

Factoring

Chapter Sections 5.1 – Factoring a Monomial from a Polynomial 5.2 – Factoring by Grouping 5.3 – Factoring Trinomials of the Form ax2 + bx + c, a = 1 5.4 – Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 5.5 – Special Factoring Formulas and a General Review of Factoring 5.6 – Solving Quadratic Equations Using Factoring 5.7 – Applications of Quadratic Equations Chapter 1 Outline

Factoring by Grouping

Factoring by Grouping The process of factoring a polynomial containing four or more terms by removing common factors from groups of terms is called factoring by grouping. Example: Factor ax + bx + by = a(x + y) + b(x + y) = (x + y)(a + b)

Factoring by Grouping Determine whether there are any factors common to all four terms. If so, factor the GCF from each of the four terms. If necessary, arrange the four terms so that the first two terms have a common factor and the last tow terms have a common factor. Use the distributive property to factor each group of two terms. Factor the GCF from the results of step 3.

Factoring by Grouping Example: a.) Factor by grouping: x2 + 3x + 4x + 12 = x (x + 3) + 4(x + 3) x + 3 is common = (x + 3)(x + 4)