Area: 65 mm2 (4X – 1) cm 10) (3x +1) m (5x – 4) m Area: 95 cm2 Area: 50 in2 (2x – 5) cm 9) (X + 3) m m (X + 8) m m X in (3x + 5) m Area: 136 in
Area: 525 m2 (2x – 7) in (2X – 1) ft X in (2X + 6) cm Clusters Factoring Cluster I: Factor each expression completely. 1) 6x5 – 9x4 2) 20x2y4 – 10x5y5 – 5xy3 3) 3xyz3 + 2x2yz3 + 5xy2z4 4) x6 – x5 5) 12x3y4z2w – 24px3y4z2 – 12x3y4z2 6) 12v6 – 15v5 7) 24x4y2z6 – 30x3y2z7 + 6x3yz6 8) 2wx5yz2 – 3wx5yz3 + 4wx5y2z2 9) f14 – f7 10) 16wqxy4z4 – 48d wxy4z4 + 64s wxy4z4 Cluster II: Factor each expression completely 1) x2 – 81 2) x2 + 8x + 16 3) 36x3 – 100x 4) 4x2 – 44x + 121 5) 6xz + 2yz – 21x – 7y 6) x2 – 225 7) x2 – 14x + 49 8) 32x3 – 2x 9) 9x2 + 84x + 196 10) 30xy – 45y +10x – 15 11) 144 – x2 12) 36x2 – 84x + 49 13) –50x3 + 18x 14) 81x2 – 72x + 16 15) 18xy + 81y – 12x – 36 Cluster III: Solve Each Equation by Factoring 1) 4x2 – 25 = 0 2) 9x2 – 6x + 1 = 0 3) 6x2 + 13x – 28 = 0 4) 10x2 – x – 2 = 0 5) 2x3 – x2 – 6x = 0 6) 16x2 – 1 = 0 7) 25x2 + 30x + 9 = 0 8) 2x2 – x – 45 = 0 9) 6x2 – x – 12 = 0 10) 12x3 – 99x2 +105x 11) 36x2 – 25 = 0 12) 49x2 – 42x + 9 = 0 13) 12x2 – 7x – 45 = 0 14) 72x2 – 11x – 6 = 0 15) 6x3 – 28x –10x = 0 Cluster IV: Find the dimensions of the given rectangles (X + 3) ft (X – 5) m m (X + 2) in X cm 1) 2) 3) 4) Area: 35 in2 Area: 33 mm2 Area: 360 cm2 Area: 130 ft2 (2x – 5) m (X -­‐ 9) in X mm (X + 4) in 5) 6) 7) 8) 2 Area: 42 m2 Answer Key Cluster I: 1) 3x4(2x – 3) 2) 5xy3(4xy – 2x3y2 – 1) 3) xyz3(3 + 2x + 5yz) 4) x5(x – 1) 5) 12x3y4z2(w – 2p – 1) 6) 3v5(4x – 5) 7) 6x3yz6(4xy – 5yz + 1) 8) wx5yz2(2 – 3z + 4y) 9) f7( f7 – 1) 10) 16wxy4z4(q – 3d + 4s) Cluster II: 1) (x + 9)(x – 9 ) 2) (x + 4)(x + 4) 3) 4x(3x – 5)(3x + 5) 4) (2x – 11)(2x – 11) 5) (3x + y)(2z – 7) 6) (x + 15)(x – 15) 7) (x – 7)(x – 7) 8) 2x(4x – 1)(4x + 1) 9) (3x + 14)(3x + 14) 10) 5(2x – 3)(3y + 1) 11) (12 – x)(12 + x) 12) (6x – 7)(6x – 7) 13) -­‐2x(5x + 3)(5x – 3) 14) (9x – 4)(9x – 4) 15) 3(2x + 9)(3y – 2) !
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Cluster III: 1) (2x + 5)(2x – 5) = 0 ; {−2 , 2 } 2) (3x – 1)(3x – 1) =0; { } !
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3) (2x + 7)(3x – 4) = 0 ; {−3 , 1 } 4) (2x – 1)(5x + 2) = 0; {− , } 5) x(x – 2)(2x + 3) = 0 ; {−1 , 0, 2} 6) (4x – 1)(4x + 1) = 0 ; {− , } !
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7) (5x + 3)(5x + 3) = 0; {− } 8) (x – 5)(2x + 9) = 0; { −4 , 5} 9) (3x + 4)(2x – 3) = 0; {−1 , 1 } !
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10) 3x(x – 7)(4x – 5) = 0; (0, 1 , 7 } 11) (6x – 5)(6x + 5) = 0; {− , } !
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12) (7x – 3)(7x – 3) = 0; { } 13) (4x – 9)(3x + 5) = 0; { −1 , 2 } !
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14) (9x + 2)(8x – 3) = 0; { − , } 15) 2x(3x + 1)(x – 5) = 0 ! !
Cluster IV: 1) x = 5; 5 in by 7 in 2) x = 12; 12 cm by 30 cm 3) x = 7; 10 ft by 13 ft 4) x = 8; 11mm by 3 mm 5) x = 10; 15 m by 35 m 6) x = 17; 17 in by 8 in 7) x =5; 5 mm by 13 mm 8) x = 6; 10 in by 5 in 9) x = 5; 19 cm by 15 cm 10) x=2; 7 m by 6 m 1 2 3 Cluster I 1 2 3 Cluster II 1 2 3 Cluster III 1 2 Cluster IV