and x2 5x + 6 = (x 2)(x 3) – – – If a 1, multiply a*c, then find 2 numbers that multiply to that product and add to b ≠ 2x2 5x 12 multiply a*c = 2 *-12 = -24; find 2 numbers that multiply to -24 and add – – to -5; they are -8 & +3. Rewrite -5x using the 2 numbers: 2x2 5x 12 = 2x2 8x + 3x 12 – – – – Now, group and GCF factor: (2x2 8x) + (3x 12) = 2x(x 4) + 3(x 4) – – – – The binomial in each set of parenthesis should be the same; it is a GCF: 2x(x 4) + 3(x 4) = (x 4)(2x + 3) – – – OPTIONAL PROBLEMS Simplify 2)
and x2 – 5x + 6 = (x – 2)(x – 3) If a ≠ 1, multiply a*c, then find 2 numbers that multiply to that product and add to b 2x2 – 5x – 12 multiply a*c = 2 *-12 = -24; find 2 numbers that multiply to -24 and add to -5; they are -8 & +3. Rewrite -5x using the 2 numbers: 2x2 – 5x – 12 = 2x2 – 8x + 3x – 12 Now, group and GCF factor: (2x2 – 8x) + (3x – 12) = 2x(x – 4) + 3(x – 4) The binomial in each set of parenthesis should be the same; it is a GCF: 2x(x – 4) + 3(x – 4) = (x – 4)(2x + 3) OPTIONAL PROBLEMS Simplify 2)
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