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CHAPTER 8 REVIEW Algebra 8 PROBLEM #1 Factor the monomial completely. -33x y 2 3 ANSWER #1 −1 ∙ 3 ∙ 11 ∙ ∙ ∙ ∙ ∙ PROBLEM #2 Find the GCF. 22b, 33c ANSWER #2 GCF: 11 PROBLEM #3 Find the GCF. 21xy, 28x y, 42xy 2 2 ANSWER #3 GCF: 7 PROBLEM #4 A landscape architect is designing a stone path 36 inches wide and 120 inches long. What is the maximum size square stone that can be used so that none of the stones have to be cut? ANSWER #4 GCF: 12 The maximum size square is 12in x 12in PROBLEM #5 Factor. 12x + 24y ANSWER #5 12( + 2) PROBLEM #6 Factor. 14x y - 21xy + 35xy 2 2 ANSWER #6 7(2 − 3 + 5) PROBLEM #7 Factor. a - 4ac + ab - 4bc 2 ANSWER #7 ( + )( − 4) PROBLEM #8 Factor. 2x - 3xz - 2xy + 3yz 2 ANSWER #8 ( − )(2 − 3) PROBLEM #9 Solve. x(3x - 6) = 0 ANSWER #9 Set each factor = 0 then solve. : {0, 2} PROBLEM #10 Solve. x = 3x 2 ANSWER #10 Bring 3x to the other side, factor, then set each factor = 0 to solve for x. : {0, 3} PROBLEM #11 Factor. x - 8x +15 2 ANSWER #11 Leading coefficient is 1 (a=1) so break down the constant. ( − 3)( − 5) PROBLEM #12 Factor. x - 5x - 6 2 ANSWER #12 Leading coefficient is 1 (a=1) so break down the constant. ( + 1)( − 6) PROBLEM #13 Solve. x - 5x - 50 = 0 2 ANSWER #13 Leading coefficient is 1 (a=1) so break down the constant. + 5 − 10 = 0 : {−5, 10} PROBLEM #14 Solve. x +12x + 32 = 0 2 ANSWER #14 Leading coefficient is 1 (a=1) so break down the constant. +4 +8 =0 : {−8, −4} PROBLEM #15 Factor the trinomial, if possible. If the trinomial cannot be factored, write prime. 12x + 22x -14 2 ANSWER #15 Factor out GCF. Leading coefficient is not 1 (a>1) so make a MAMA chart. 2 2 − 1 3 + 7 PROBLEM #16 Factor the trinomial, if possible. If the trinomial cannot be factored, write prime. 2a +13a - 24 2 ANSWER #16 Leading coefficient is not 1 (a>1) so make a MAMA chart. + 8 2 − 3 PROBLEM #17 Solve each equation. Check your solutions. 6x - 7x - 5 = 0 2 ANSWER #17 Leading coefficient is not 1 (a>1) so make a MAMA chart. 3 − 5 2 + 1 = 0 1 5 : {− , } 2 3 PROBLEM #18 Solve each equation. Check your solutions. 40x + 2x = 24 2 ANSWER #18 Bring over 24 to the other side. Factor out GCF Leading coefficient is not 1 (a>1) so make a MAMA chart. 2 5 + 4 4 − 3 PROBLEM #19 Factor each polynomial. 3x - 3 2 ANSWER #19 Factor out GCF. 3( 2 − 1) Now you have difference of two perfect squares so break down further. 3( + 1)( − 1) PROBLEM #20 Factor each polynomial. 16a - 21b 2 2 ANSWER #20 Prime PROBLEM #21 Solve by factoring. Check your solutions. 9x - 25 = 0 2 ANSWER #21 3 + 5 3 − 5 = 0 5 5 : {− , } 3 3 PROBLEM #22 Solve by factoring. Check your solutions. x - 4 =12 2 ANSWER #22 +4 −4 =0 : {−4, 4} PROBLEM #23 Factor each polynomial, if possible. If the polynomial cannot be factored write prime. x + 5x + 25 2 ANSWER #23 Prime PROBLEM #24 Factor each polynomial, if possible. If the polynomial cannot be factored write prime. 4 - 28a + 49a 2 ANSWER #24 Perfect square trinomial 2 − 7 2 PROBLEM #25 Factor each polynomial, if possible. If the polynomial cannot be factored write prime. x -16x 4 2 ANSWER #25 Factor out GCF. 2 ( 2 − 4) Then you have difference of two perfect squares, so factor more. 2 ( + 2)( − 2) PROBLEM #26 Solve each equation. Check your solutions. 4y = 64 2 ANSWER #26 Bring 64 to the other side. Factor out GCF. 4 2 − 16 = 0 Then you have difference of two perfect squares, so factor more. 4 −4 +4 =0 Set each factor = 0 and solve for y. : {−4, 4} PROBLEM #27 Solve each equation. Check your solutions. (x - 9) =144 2 ANSWER #27 FOIL left side and bring 144 to the other side. You have a trinomial where a=1, so break down c. + 3 − 21 = 0 Then, set each factor =0 and solve for x. : {−3, 21} PROBLEM #28 A sidewalk of equal width is built around a square yard. What is the width of the sidewalk? ANSWER #28 6 + 2 2 = 900 36 + 24 + 4 2 = 900 −864 + 24 + 4 2 = 0 4 2 + 24 − 864 = 0 4 2 + 6 − 216 = 0 4 − 12 − 18 = 0 : {12, 18}