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6.2 Solving by Factoring Worksheet MPM2D Jensen 1. Solve a) 𝑥 + 5 𝑥 + 2 = 0 b) 𝑥 − 3 𝑥 + 4 = 0 c) 𝑥 − 1 𝑥 − 7 = 0 d) 𝑥 𝑥 + 9 = 0 e) 2𝑥 + 3 𝑥 − 5 = 0 f) 2𝑥 − 1 3𝑥 + 4 = 0 2. Solve by factoring a) 𝑥! + 8𝑥 + 12 = 0 b) ℎ! + 9ℎ + 18 = 0 c) 𝑚! + 3𝑚 = 0 d) 𝑤! − 18𝑤 + 56 = 0 e) 𝑥! − 2𝑥 = 0 f) 𝑐! − 17𝑐 + 30 = 0
3. Solve a) 3𝑥! + 28𝑥 + 9 = 0 b) 4𝑘! + 19𝑘 + 15 = 0 d) 16𝑏! − 1 = 0 f) 4𝑥! − 12𝑥 + 9 = 0 4. Solve a) 𝑥! + 5𝑥 = −4 c) 𝑘! = 13𝑘 − 12 = 0 e) 𝑚! = 300− 20𝑚 f) 𝑦! = 7𝑦
5. Solve a) 2𝑚! = −7𝑚 − 6 b) 9𝑥! = 𝑥 + 8 d) −5 = 2𝑝 − 16𝑝! f) 3𝑤! + 22𝑤 = −7 6. Solve a) −𝑥! − 10𝑥 − 16 = 0 b) 3𝑡! + 24𝑡 + 45 = 0 c) 6𝑑! + 15𝑑 = −9 d) −10𝑔! + 32𝑔 = 6
7. A basketball is tossed from the top of a 3 meter wall. The path of the basketball is defined by the relation 𝑦 = −𝑥! + 2𝑥 + 3, where x represents the horizontal distance travelled, on meters, and y represents the height, in meters, above the ground. How far has the basketball travelled horizontally when it lands on the ground? 8. A rectangle has dimensions x+10 and 2x-‐3. Determine the value of x that gives an area of 54 cm2
Answers: 1) a) -‐5, -‐2 b) 3, -‐4 c) 1, 7 d) 0, -‐9 e) !!
!, 5 f) !
!, !!!
2) a) -‐2, -‐6 b) -‐3, -‐6 c) 0, -‐3 d) 14, 4 e) 0, 2 f) 15, 2 3) a) !!
!, 9 b) -‐1, !!"
! d) !
! , !!! f) !
!
4) a) -‐1, -‐4 c) 12, 1 e) 10,-‐30 f) 0, 7 5) a) !!
!, -‐2 b) 1, !!
! d) !!
!, !! f) !!
!,−7
6) a) -‐8, -‐2 b) -‐3, -‐5 c) -‐1, !!
! d) !
!, 3
7) 3 meters 8) 3.5 cm
