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Unit 2 – Day 3 - Common Factoring To factor an expression is to write it as a product. It is the opposite of ________________________. Common Factoring is the easiest type of factoring. It will always be the method of factoring that should be attempted ___________. Ex. 1 Find the GCF. a) 24, 36, 60 b) 4x2, 10x3, 8x4 c) 2a(a - 3), 5(a - 3) Ex. 2: Determine the greatest common factor. Use the GCF to factor the expression. a) 3a - 9 b) x2 + 2x c) 5a2 + 10a e) 10x3 - 15x2 f) 3x2y + 12xy g) 15a3b4c + 20a2b5c3 Ex. 3: Factors can sometimes be polynomials i) a (2x+1)+b (2x+1) ii) 2(a +b)-3c (a +b) Ex. 4: Factor by grouping i) bx + 3x + by + 3y Ex. 5 Determine the unknown measurement. Pg 93 # 2, 3, 5 – 9, 11, 15, 16 d) 2x3 + 6x2 - 12x ii) 9m + 12 - 15m2 - 20m iii) 4(r -t) -3s (t -r) Warm up Factor. 1) 5b - 10 3) 14x4 - 21x3 2) -8a + 12 4) 6a5b4 - 12a3b3 + 18a4b2 Unit 2 Day 4: Factoring Trinomials: x2 + bx + c (x + 2)(x + 1) = Steps for factoring trinomials of the form x2 + bx + c 1) Write two brackets with x at the front of each. 2) Fill in two numbers that - 3) Check by expanding. ** Remember to pay attention to the signs!! If numbers multiply to give a negative we know If numbers multiply to a positive we know Examples: Factor. (Remember to common factor first if possible!) 1) x2 - 4x + 3 4) a2 - 4a – 21 7) 3x2 - 12x 2) x2 + 14x + 40 5) n2 - n - 30 8) 2m2 + 10m – 48 3) x2 - 7x + 12 6) x2 + 2xy - 48y2 9) 4y2 - 8y – 60 10) c2 – 10c + 25 pg 99 # 2, 3, 5, 6, 7, 9, 14 Warm Up Factor a) x2 - x - 6 b) x2 + x – 6 c) 2x2 - 18x + 40 Unit 2 Day 5: Factoring Tricky Trinomials Factor completely 4x2 - 8x - 12 common factor sum & product Not so tricky... but! Factor 2n2 + 7n + 6 Method 1: Factor using a chart. 2n2 + 7n + 6 Method 2: Factor using decomposition. 2n2 + 7n + 6 Examples: Factor a) 3a2 - 17a + 20 b) 6p2 + 11p – 10 c) 16m2 – 26mn – 12n2 d) 5k2 – 17k - 4 Question: 5x - 4 is a factor of 5x2 + 26x - 24. What is the other factor? How can you check to see if you have factored correctly? p. 109 # 2, 4 – 6, 9, 10, 13, 14 Warm up Factor 1) x2 - 6x + 9 2) 4x2 + 12x + 9 Unit 2 Day 6 – Special Quadratics Perfect Square Trinomials Factor 1) t2 -12t + 36 2) 25y2 + 40yz + 16z2 Pattern: Difference of Squares Factor x2 - 25 Pattern: Factor 1) 49y2 - 36 2) 36 - 9k2 3) 28x2 - 175y2 pg. 115 #2, 3, 4, 7, 11 4) a4 - 16 Unit 7 Review 1) Expand and simplify a) 2x(3x - 1) + 4(x2 + 3x + 3) - 2x(5x - 3) b) 2(x + 1)(3x - 7) - (x + 3)2 2) Factor fully. a) x2 + 2x - 35 b) 9x – 36 c) 3x2 + 14x +8 d) x2 + xy + 2x + 2y e) 2x3 - 6xy + 10x f) 4x2 + 16x - 48 g) 2x2 – 50 h) 9x2 - y2 i) 6a3 - 4a2 - 16a j) 16x2 - 24x + 9 k) (x+y)2 - 7(x+y) – 18 l) (x + 5)2 - (3x - 2)2 3) Determine the length of the rectangle, given the area and the width. x-5 3x A = 6x2 + 15x A = x2 - 15x + 50 4) Determine two possible values of k to make each expression factorable. a) x2 + kx + 12 b) x2 - 2x + k