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Investigation: Basic Factoring Factoring is undoing multiplication, almost like division. Part 1: Factoring with Numbers Step 1: Factor by making a factor tree: a. 108 b. 200 Step 2: What is the greatest common factor between a. 108 and 200 b. 200 and 36 c. 36 c. 108 and 36 Part 2: How to factor out the GCF. Step 1: Simplify the following. Put your answer in standard form. a. 8(3) = b. 4(3 + 2) = c. 2x(5 – x) = d. 3t2(4t3 + 7) = e. -(n + 3) = f. (9m3 – 8m4 + 6m)(-7m2) = Step 2: Complete each statement by factoring out the greatest common factor. a. 4x2 + 20x – 12 = _____ (x2 + 5x – 3) b. 9n2 – 24n = 3n( ________________) c. 9x2 + 3x – 18 = __________ (_______________________________) d. 7p2 + 21 = ___________________________________ e. 4w3 + 2w2 = f. 18x2y3z – 24x2yz + 6xy2z + 8xyz = g**. 3x(x + 3) + 2(x + 3) = Step 3: Now simplify each of the following. Put your answer in standard form. What do you notice about the relationship between the middle term and the last term? a. (x – 5)(x + 3) = b. (x - 4)(x – 1) = c. (x + 2)(x + 7) = d. (x + 4)(x – 9) = Step 4: Now complete each statement to factor. Check your answers by multiplying the factors. a. x2 + 8x + 7 = (x + 1)(x + ___) b. x2 + 6x + 8 = (x + 2)(___ + ____) c. x2 + 12x + 32 = (_____________)(x + 4) d. x2 + 14x + 40 = (________________)(________________) e. x2 – 17x + 72 = (x – 9)(_____________________) f. x2 – 6x + 8 = (__________________)(x – 4) g. x2 – 7x + 12 = (_____________________)(___________________) h. x2 – 11x + 24 = i. x2 – x – 12 = (x – 4)(____________________) j. x2 – 14x – 32 = (x + 2)(_______________________) k. x2 + 9x – 10 = (____________________)(___________________________) l. x2 + 4x – 5 = m. 3x2 – 9x – 84 = Step 5: Now simplify these. Put your answer in standard form. a. (2x – 7)2 b. (4x + 3)(4x – 3) c. (x – 9)(x + 9) d. (5x + 4)2 Step 6: Factor each of the following. a. 9x2 – 42x + 49 = (_____________)(________________) b. 4x2 + 12x + 9 = c. 64x2 – 16x + 1 = d. 25x2 + 90x + 81 e. x2 – 64 f. 4a2 - 49 Step 7: In general when factoring an expression of the form x2 + bx + c, you want to try to find 2 numbers that (multiply/add) ________ to b and (multiply/add) ________ to c. a2 + 2ab + b2 = ____________________ is called a perfect square trinomial. a2 – b2 = __________________ is called a difference of squares. Step 8: Put it all together. Factor. a. 15x3y5z2 – 30x2y7z + 20x2y3z5 – 5x2y3z b. 3x(x +2) + 7(x + 2) c. 3x2+ 12x - 63 d. 100x2 - 49 e. 9x2 + 30xy + 25y2 f. x2 – 12x - 32