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MBF3C Date: _________________________ Factoring – Greatest Common Factor REVIEW TYPES OF FACTORING 1. Trinomial Factoring i.e. x2 + 8x + 12 2. Perfect Square Trinomial i.e. x2 – 10x + 25 Find two numbers that multiply to 25 and add to -10. = (x – 5)(x – 5) Since the two brackets are the same, write it as = (x – 5)2 squared i.e. x2 – 121 Take the square root of each term = (x + 11)(x – 11) The square root can be a positive or negative number 3. Difference of Squares Find two numbers that multiply to 12 and add to 8 = (x + 2)(x + 6) GREATEST COMMON FACTOR (x2 + bx) Method 1 Rewrite the Polynomial in the form x2 + bx + c c Find two numbers that multiply to ______ and b add to _______ i.e. x2 + 5x = x2 + 5x + 0 in this case c = 0 = x2 + 5x + 0 = (x + 0)(x + 5) = x (x + 5) EXAMPLES 1. x2 + 15x = x(x + 15) find 2 numbers that multiply to zero and add to 5 Method 2 Find the Greatest Common Factor factor The largest ___________ by which you can divide ______________ ALL terms in a polynomial x i.e. x2 + 5x GCF = _______ = x2 + 5x remove one x from each term, as it is common = x (x + 5) 2. 4x2 – 8 = 4(x2 – 2) 3. 3x2 + 18x = 3x(x + 6) FULLY FACTORING TRINOMIALS of the FORM ax2 +bx + c 4x2 – 8x – 60 = 4(4x2 – 8x – 60) 4 4 4 GCF = 4 first pull out the GCF and divide each term by it Steps to Fully Factoring (in this order) = 4(x2 – 2x – 15) This can be factored further a. Is it a difference of squares? = 4(x – 5)(x + 3) Find two numbers that multiply to -15 and add to -2 b. Is it a perfect square trinomial? 1. Always look for a common factor first 2. Can it be factored further? c. Are there two numbers which multiply to c and add to b?