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Factoring Review Binomials Look for the Greatest Common Factor 18x + 27 GCF = 9 9(2x + 3) Binomials No GCF look for the difference of squares x 9 2 This means that the two terms of the binomial are perfect squares and there is a minus sign between them. Binomials You are done factoring a binomial: • When you have the sum of squares • When there are no more perfect squares • When there is no longer a squared term Trinomials • Look for the GCF • Determine what the signs are – If the last term is positive the signs are both the same as the middle term – If the last term is negative the signs are opposite (one is positive and one is negative) Trinomials • Look at the first term. If there is not a number in front of the squared term then you only need to look at factors of the last term that will add or subtract to get the middle term. Trinomials x 10 x 16 2 • (x + 8)(x + 2) • • • • • List Factors of 16 16,1 4,4 8,2 Which ones add together to give you 10? Trinomials x 5 x 36 2 • (x – 9)(x + 4) • List Factors of – 36 • • • • • • • • • • -1,36 -36,1 -12,3 -3,12 -18,2 -2,18 -4,9 -9,4 -6,6 Which pair add up to – 5? Trinomials • Look at the first term. If there is a number in front of the squared term, you must look at factors of the first term and the last term. If there is a small amount of factors you can easily guess and check. Trinomials • This is the long way, but this always works! 6 x 17 x 12 2 • • • • • • • • First multiply 6 by 12 Find factors of 72 36,2 24,3 4,18 6,12 8,9 Which pair add to get 17? Trinomials • Break the 17x into the two numbers 6 x 8 x 9 x 12 2 • Then Group the 1st two terms and the last two terms. (6 x 8x) (9 x 12) 2 Trinomials • Factor out the GCF in each set of parenthesis. • 2x(3x + 4) + 3(3x + 4) • Both sets of numbers in the parenthesis have to be exactly the same to continue. Trinomials • The numbers in front of the parenthesis make up one factor and the parenthesis make up the other factor. • (2x + 3)(3X + 4) Trinomials • Always factor completely! – You may have binomials that can be factored further.