Aside from whole numbers, algebraic expressions are also used to represent areas and dimensions. For example, if the dimensions of a rectangular garden are x + 3 and x + 4, then the area of the garden is x² + 7x + 12 square units. In this example, x + 3 and x + 4 are the factors of x² + 7x + 12. Factoring is the process of writing polynomials as a product of two or more numbers or terms. X² + 7x + 12 = (x+3)(x+4) product factors One technique to write a polynomial expression in factored form is look for its greatest common factor (GCF). This GCF is factored out and multiplied to the remaining tems in the expession. Examples: Express as a product of two or more terms. 1. 6x-9 2.4y5-24y³ Solution: Factor out the GCF of each polynomial the desired product. 3. 15ab²+ 10a²b above. The other factor is the expression multiplied to the GCF to give 2.4y³(y²-6) GCF: 4y³ 3. 5ab(3b + 2a) GCF: 5ab 1. 3(2x-3) GCF: 3 The process of writing a polynomial by factoring out a monomial factor common to all the terms is called common monomial factoring. If each of the factors cannot be factored any further, then we say that the polynomial is factored completely. Express as a product of two or more terms.Write your answer on the blank. 1. 2b(x+3) - 5(x+3) 2. (mn + 1)(y-2) + (n − 1)(y-2)
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