University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2021
Views:

421

Pages:

7
Author:

Adriel Kelley

Algebra Name ___________ Unit 6 Review Complete the following concept questions What is the first step to every factoring problem? ime If a problem cannot be factored, what is the answer? ran ssi ; ve What is the difference between factoring and solving? ve Explain why (x^2 + 36) is not a DOTS problem. not a difference What is the name of the property used to solve by factoring? 1 1. www.cbsd.org www.cbsd.org Factor each polynomial. Each of these polynomials will only be one type of factoring. (Two are prime.) (x^2 - 16) ((x+4)(x-4)) (40 + 13x + x^2) (x^2 + 13x + 40) ((x+8)(x+5)) (x^2 - 16x + 64) ((x-8)^2) (3x^2 + 17x + 10) (3x^2 + 15x + 2x + 10) (3x(x+5) + 2(x+5)) ((x+5)(3x+2)) (4x^2 + 16x) (4x(x+4)) (25 - 9x^2) (05+9x) ((5+3x)(5-3x)) (x^2(y-7) + 3(y-7)) ((y-7)(x^2+3)) (x^2 - 6x + 10) prime (10x^2 - 27x + 5) (10x^2 - 25x - 2x + 5) (5x(2x-5) - 1(2x-5)) ((2x-5)(5x-1)) (12x^3 + 15x^2 - 8x - 10) (3x^2(4x+5) - 2(4x+5)) ((4x+5)(3x^2-2)) (-8x^2 + 4x) (-4x(2x-1)) (4+x^2) prime Factor the following polynomials completely. Show your work. None are prime. (8x^3 - 18x) (2x(4x^2-9)) (2x(2x+3)(2x-3)) (2x^2 - 20x + 32) (2(x^2 - 10x + 16)) (2(x-2)(x-8)) (-3x^2 + 15x + 42) (-3(x^2 - 5x - 14)) (-3(x-7)(x+2)) (4x^3 + 8x^2 + 3x) (x(4x^2 + 8x + 3)) (x(4x^2 + 2x + 6x + 3)) (x[2x(2x+1) + 3(2x+1)]) (x(2x+1)(2x+3)) (x^3 + 3x^2 - 100x - 300) (x^2(x+3) - 100(x+3)) ((x+3)(x^2 - 100)) ((x+3)(x+10)(x-10)) (ax^2 + 6ax - 7a) (a(x^2 + 6x - 7)) (a(x+7)(x-1)) Solve each equation by factoring. Show your work. None are prime. (36x^2 - 1 = 0) ((6x+1)(6x-1) = 0) (6x+1=0) (6x-1=0) (6x=-1) (6x=1) (x = -\frac{1}{6}) (x = \frac{1}{6}) (x = \pm \frac{1}{6}) (2x^2 + 22x = -56) (2x^2 + 22x + 56 = 0) (2(x^2 + 11x + 28) = 0) (2(x+4)(x+7) = 0) (x+4=0) (x+7=0) (x=-4) (x=-7) (x = -4, -7) (-8x^2 + 48x = 0) (-8x(x-6) = 0) (-8x=0) (x-6=0) (x=0) (x=6) (x = 0, 6) (3x^2 - 17x + 7 = 2x + 1) (3x^2 - 19x + 6 = 0) (3x^2 - 18x - 1x + 6 = 0) (3x(x-6) - 1(x-6) = 0) ((x-6)(3x-1) = 0) (x-6 = 0) (3x-1 = 0) (x = 6) (x = \frac{1}{3}) (4x^3 + 12x^2 - x = 3) (4x^3 + 12x^2 - x - 3 = 0) (4x^2(x+3) - 1(x+3) = 0) ((x+3)(4x^2 - 1) = 0) ((x+3)(2x+1)(2x-1) = 0) (x+3 = 0) (2x+1 = 0) (2x-1 = 0) (x = -3) (x = -\frac{1}{2}) (x = \frac{1}{2}) (-2x^2 + 95 = -3) (-2x^2 + 98 = 0) (-2(x^2 - 49) = 0) (-2(x+7)(x-7) = 0) (x+7 = 0) (x-7 = 0) (x = \pm 7) Define your variables, set up an equation, and then solve. Label your final answers. The sum of a positive number and its square is 56. Find the number. (x^2 + x = 56) (x^2 + x - 56 = 0) ((x+8)(x-7) = 0) (x = 7) The length of a rectangle is 5 inches more than the width. The area of the rectangle is 66 in². Find the dimensions of the rectangle. (x(x+5) = 66) (x^2 + 5x = 66) (x^2 + 5x - 66 = 0) ((x+11)(x-6) = 0) length: 11 in. width: 6 in. The product of two consecutive negative even integers is 360. Find the integers. (x(x+2) = 360) (x^2 + 2x = 360) (x^2 + 2x - 360 = 0) ((x+20)(x-18) = 0) -20, -18 Eight less than the square of a positive number is the same as 2 times the number. Find the number. (x^2 - 8 = 2x) (x^2 - 2x - 8 = 0) ((x-4)(x+2) = 0) (x = 4)