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Reviewing Concepts • Lesson 29(3) will review the following concepts: • Dividing Exponent laws • Dividing Polynomial by a Monomial • Expanding Binomials ( FOIL) • Factoring out the monomial (GCF) • Factoring Trinomials EXPONENT LAW 3 • QUOTIENT OF POWERS • xa xb = xa-b Dividing Powers with the same base 6a5b3 3a2b2 Solution 6a5b3 means 3a2b2 6a5b3 3a2b2 = 6 a5 b3 x 2 x 2 3 a b 6 a5 b3 x 2 x 2 3 a b = 2a3b Dividing a Polynomial by a Monomial Divide 18mn – 4n + 2n2 by 2n. 18mn – 4n + 2n2 2n 18mn – 4n + 2n 2n 2n 2n2 9m – 2 + n Remember your Exponent Laws for Division Simply divide each term by 2n Expanding Binomials Example: (x – 2)(x + 3) F – Fist (x – 2)(x + 3) O – Outside (x – 2)(x + 3) I – Inside (x – 2)(x + 3) L – Last (x – 2)(x + 3) (x)(x) + (x)(3) + (-2)(x) + (-2)(3) x2 + 3x – 2x – 6 x2 + x - 6 Factoring out the GCF Factor: 4t + 12 Step 1 – Find the GCF 4t = 4 * t 12 = 4 * 3 GCF = 4 Step 2 – Divide to find the other factor 4t + 12 = t+3 4 Therefore 4t + 12 = 4(t + 3) Check by expanding 4(t + 3) 4(t) +4(3) = 4t + 12 Factoring Trinomials x2 + 7x + 6 What two numbers add up to +7 Factors: Same two numbers that multiply to give you +6 Therefore: x2 + 7x + 6 = (x + 1)(x + 6) Sum: 1x6 1+6=7 -1 x -6 -1 + (-6) = - 7 2x3 2+3=5 -2 x -3 -2 + (-3) = - 5 Chart to Help with Signs in Factoring Trinomials Sum (• 2nd Term) Negative Product ( 3rd Term) Negative Negative Positive Positive Negative Positive Positive INTEGERS Bigger #(-) Smaller # (+) Both Negative numbers Bigger # (+) Smaller # (-) Both Numbers Positive SIMPLIFY 4x5y3 2x2y2 -8a6c3 2a2c DIVIDE 30xy2 – 15x + 5y 10y2 6ab – 4a + 8b2 4a EXPAND (x – 5)(x + 6) (x – 2)(x - 3) (x + 5)(x + 7) TAKE OUT THE COMMON FACTOR 6t + 12 6t2 + 12t - 18 -3x2 + 6x - 18 FACTOR COMPLETELY x2 + 7x + 6 x2 - 8x - 16 x2 + 4x - 12 Class work • Check solutions to lesson 29(2) • Complete Lesson 29(3) worksheet.