Factoring - Factoring Factoring is the opposite of multiplying Factor a monomial from a polynomial 1 Determine the GCF of all terms in the polynomial 2

Factoring - Factoring Factoring is the opposite of...

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Unformatted text preview: Factoring Factoring is the opposite of multiplying Factor a monomial from a polynomial 1. Determine the GCF of all terms in the polynomial 2. Write each term as the product of the GCF and another factor. 3. Use the distributive property to factor out the GCF. Examples Factor out the greatest common factor in the expression . 2 12 x 4 x 8 GCF Factor out the GCF 4 9 5 60 x 6 x 18 x y 2 To factor four terms by grouping 1. Arrange the four terms into two groups of two terms each. Each group of two terms must have a GCF. 2. Factor the GCF from each group of two terms. 3. If the two terms formed in step 2 have a GCF, factor it out. Factor by grouping 2 5 x xy 20 xy 4 y 2 Factor by grouping 2 12 x 8 xy 15 xy 10 y 2 Factor by grouping 3 2 5a 15a 10a 30 Factoring trinomials- part 1 To factor trinomials of the form 2 x bx c 1. find two numbers whose product is c and whose sum is b. 2. the factors of the trinomial will be (x + 1st number)(x+2nd number) Examples We need factors of 30 whose sum is -17 2 x 17 x 30 Example 2 2 x 6 x 91 Example 3 2 x 34 x 64 Factoring trinomials –part 2 To factor trinomials of the form 2 ax bx c Using trial and error: 1. write all pairs of factors of the coefficient of the squared term, a. 2. Write all pairs of factors of the constant, c. 3. Try various combinations of these factors until the correct middle term, bx, is found. examples 2 3 x 11 x 20 Example 2 2 4a 43a 30 More examples 2 6c 11c 10 ...
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