Chapter 1: Factoring and Quadratic Equations

Chapter 1: Factoring and Quadratic Equations Section 1.1: The Greatest Common Factor #1-8: Factor out the GCF. 1) 2y – 10 2) 6x – 12 3) 14x3 – 7x2 + 7x 4) 25y3 – 20y2 + 5y 5) b5 – 3b4 + b3 6) x3 – x2 + 9x 7) 12x4 – 3x3 8) 3y3 – y2 #9-14: Factor out a (-1) from each polynomial. 9) -x + 2 10) -3x – 5 11) 3 – x 12) 5 – x 13) 9 – 5x 14) 16 – 7w #15-20: Factor each polynomial by factoring out the opposite of the GCF. 15) -4x3 + 12x2 16) -20y2 – 15y 17) -12x3 + 4x2 – 8x 18) -42a5 + 24a3 – 4a 19) 6 – 3z 20) 10 – 5y 3 Chapter 1: Factoring and Quadratic Equations Section 1.2: Factoring Trinomials of the Form x2 + bx + c #1-14: Factor each trinomial, state if a polynomial is prime. 1) x2 + 3x – 18 2) y2 + 5y – 50 3) c2 + 12c + 20 4) b2 + 6b + 9 5) r2 + 6r + 8 6) x2 + 13x + 36 7) y2 – 10y +16 8) z2 – 7z + 12 9) x2 + x – 20 10) y2 – 5y – 6 11) x2 + x + 3 12) y2 + 5y + 11 13) b2 + 3b – 5 14) a2 + 7a – 3 #15-30: Factor each trinomial. Make sure to factor out a negative or the GCF where applicable. 15) -x2 – 7x –10 16) -y2 – y + 30 17) -w2 + 18w – 77 18) –b2 + 14b – 33 19) 3x2 +12x –36 20) 6y2 + 30y + 24 21) 6z2 – 30z + 24 22) 4x2 + 40x – 44 23) x3 + 6x2 –7x 24) y3 – 5y2 + 6y 25) -2x3 – 10x2 + 12x 26) -2y3 – 10y2 + 48y 27) 10y + 9 + y2 28) 5y – 14 + y2 29) 10z + z2 + 15 30) 3z + z2 – 18 4 Chapter 1: Factoring and Quadratic Equations Section 1.3: Factoring Trinomials in the Form ax2 + bx + c where a 1 #1-16: Factor, (if a polynomial is prime, say so) 1) 3x2 + 10x + 7 2) 5x2 + 12x + 7 3) 5x2 + 13x + 6 4) 6x2 + 23x + 7 5) 3x2 – 11x + 10 6) 5x2 – 17x + 12 7) 2b2 – 15b + 7 8) 3w2 – 14w + 8 9) 6y2 – 7y – 5 10) 8y2 – 6y – 5 11) 8a2 + a – 7 12) 4x2 + 4x – 15 13) 2x2 – 5x – 7 14) 8y2 – 5y – 3 15) 3x2 + 5x + 6 16) 7x2 + x + 3 #17-24: Factor, remove the GCF first 17) 4m2 + 34m – 18 18) 15n2 + 36n + 21 19) 4z3 – 13z2 + 3z 20) 8x3 – 22x2 + 5x 21) 20x3 – 18x2 + 4x 22) 18y3 – 39y2 + 6y 23) -16x2 + 44x – 10 24) -20x2 + 18x – 4 5 Chapter 1: Factoring and Quadratic Equations Section 1.4 Factoring Binomials #1- 14: Completely factor the binomials, remember to factor out the GCF first when applicable (if a problem is prime say so). 1) x2 – 9 2.) y2 – 81 3) 25a2 – 81 4) 16b2 – 49 5) x3 – 64x 6) x5 – 121x3 7) 9 – x2 8) 49 – y2 9) x4 – 16 10) y4 – 81 11) x2 + 4 12) y2 + 9 13) 2b2 + 50 14) 3x2 + 12 #15-24: Completely factor the binomials, remember to factor out the GCF first when applicable (if a problem is prime say so). 15) x3 + 8 16) y3 + 64 17) b3 + 27 18) x3 + 125 19) x3 – 64 20) y3 – 27 21) 8x3 – 27 22) 125x3 – 64 23) 16x3 – 54 24) 3x3 – 81 6 Chapter 1: Factoring and Quadratic Equations Section 1.5 Solving Quadratic Equations by Factoring #1 - 6: Solve each equation. 1) (x-3)(x+2)=0 2) (x+3)(x – 5) = 0 3) (2x – 1)(3x+4) = 0 4) (2x–3)(4x+5) = 0 5) x(x – 1)(x+2) = 0 6) 2x(x–3)(x+5) = 0 #7 - 18: Solve each equation. 7) x2 – 5x + 6 = 0 8) x2 – 14x + 45 = 0 9) x2 + 6x – 7 = 0 10) x2 – 5x – 6 = 0 11) y2 – 81 = 0 12) b2 – 25 = 0 13) 25x2 – 16 = 0 14) 49y2 – 16 = 0 15) 3x2 + 5x + 2 =0 16) 5x2 + 9x + 4 =0 17) 2x2 + 3x + 1 = 0 18) 3x2 – 5x – 2 = 0 #19 - 24: Solve each equation. (Remember to factor out the GCF first) 19) 3x3 + 5x2 + 2x = 0 20) 10x3 + 18x2 + 8x = 0 21) 4x2 + 2x – 6 = 0 22) 3x2 + 18x – 21 = 0 23) 5x2 – 20 = 0 24) 2x2 – 18 = 0 #25 - 32: Solve each equation. 25) r(r+1) = 12 26) x(x–1) = 6 27) (x – 2)(x – 3)= 6 28) (x – 1)(x– 2) = 12 29) x(x – 3) +2 = 30 30) 3x(x – 1) – 4 = 2 31) 2x(x – 3) = 5x(x– 4) +8 32) 2(3 – 4x) = x(x – 1) – 2 7 Chapter 1: Factoring and Quadratic Equations Chapter 1: Review 1) Completely factor the polynomial. State if a polynomial is prime. a) x2 + 7x – 18 b) z2 – 13z + 36 c) -y2 +5y + 14 d) -2y3 – 10y2 + 48y e) 6x2 + 13x + 5 f) x2 + 2x + 3 g) 9n2 + 24n + 15 h) 4x3 – 16x2 – 84x i) 25b2 – 81 j) x2 + 64 k) x3 + 125 l) 27y3 – 64 m) 5m2 + m - 6 n) 3n2 + 7n +2 o) -3x3 – 21x2 + 54x p) 25b2 + 30b + 9 2) Solve each equation. a) 2x(x– 3) = 0 b) (x+2)(3x – 10)=0 c) x2 – 3x – 10 = 0 d) 5x2 + 16x + 3 =0 e) x(x– 1) = 20 f) 3x(x – 1) – 4 = 14 g) a2 – 49 = 0 h) 25b2 = 16 i) 2x2 + 3x + 1 = 0 j) x(x – 2) = 0 k) y2 + 6y + 9 = 0 l) b2 + 6b = 7 8