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

2021
Views:

302

Pages:

2
Author:

Kieran Caldwell

REVIEW:Polynomial Operations I will be able to add, subtract, multiply, and divide polynomials, KEY Name Per Part 1: Classify each as M (monomial), B (binomial), T (trinomial), P (polynomial), or C (constant). B 2x + 1 2) B * 17x ^ 2 + 11 3). P = 8x ^ 3 + 2x ^ 2 + 3x - 7 4). C -130 5). 4a ^ 2 + 7a - 10 6). 10x ^ 3 - 2x + 1 Part 2: Order of Operations and Fractions 7.) 4 + 2 * 12 / 6 - 8 = 4 + 24/6 - 8 4+4-8 8 - 8 = boxed 0 8.) 9/3 + 6 * 2 = 3 + 6z 3+12 15 9) 3 + 4 - 6 + 2 * 35 = 3 + 4 - 6 + 70 170 10.) 2/7 + 3/7 = (2 + 3)/7 = boxed 5 7 11.) 4/5 + 1/2 = 8/10 + 5/10 = |13/10| 12.) 3/5 - 1/3 = 9/15 - 5/15 = boxed 4 15 Part 3: Add these polynomials. Only combine things that are alike (have the same exponent). 12.) (19x ^ 2 + 12x + 12) + (7x ^ 2 + 10x + 13) ( 19x + 12x + 12x +12|+7x^ 2 +10x+13) 21p * x ^ 2 + 22x + 25 13.) (4x ^ 2 - 6x + 7) + (- 19x ^ 2 - 15x - 18) 4x ^ 2 - x + 7 - 19x ^ 2 - 15x - 18 - 15x ^ 2 - 21x - 11 14.) (20x ^ 2 + 15x + 13) + (- 19x ^ 2 + 17x + 5) 20x ^ 2 + 15x + 13 - 19x ^ 2 + 17x + 5 x ^ 2 + 32x + 18 Part 4: Subtract these polynomials. 18.) (6x + 14) - (9x + 5) 6x + 14 - 9x - 5 - 3x + 4 21.) (17x ^ 2 + 7x - 14) - (- 6x ^ 2 - 5x - 18) 17x ^ 2 + 7x - 14 + 6x ^ 2 + 5x + 18 23x ^ 2 + 12x + 4 15.) (9x ^ 5 - 4x ^ 1) + (10x ^ 5 - 15x ^ 4 + 14) 1x ^ 4 - 4x ^ 5 + 10x ^ 5 - 15x ^ 4 + 14 9x ^ 6 + 6x ^ 5 - 15x ^ 4 + 14 20.) (19x ^ 2 + 9x + 16)(5x ^ 2 + 12x + 7) + 2 19x ^ 2 + 9x + 16 - 5x ^ 2 - 12x - 7 14x ^ 2 - 3x + 9 22.) (- 18x ^ 2 + 4x - 16) - (15x ^ 2 + 4x - 1) - 18x ^ 2 + 4x - 16 - 15x ^ 2 - 4x + 1 - 33x ^ 2 - 15 Part 5: Use the distributive property to find the product (multiply). 29.) 6(x ^ 2 + 2x + 7) 6x ^ 2 + 12x +42| 30.) 4x(1 - x) 4x - 4x ^ 2 30.) - x ^ 2 * (x + 5) x ^ 3 - 5x ^ 2 31.) 3x ^ 2 * (4x ^ 2 - 5x + 10) 12x ^ 5 - 15x ^ 3 + 30x ^ 2 32.) 3x(- x ^ 2 + 2x - 12) - 3x ^ 3 + 6x ^ 2 - 36x Part 7: Use division and the distributive property to simplify. Divide EVERY term. 33.) (- 15x + 10)/5 (- 15x)/5 + 10/5 - 3x + 2 35.) (- 18x ^ 2 + 21x)/- 3 (- 16x ^ 2)/- 3 + (21x)/- 3 6x ^ 2 - 7x 37.) (20x ^ 4 + 15x ^ 2)/(5x ^ 7) (20x ^ 4)/(5x ^ 2) + 15x^ prime2 5x^ 2 4x ^ 2 + 3 ] 38.) (x ^ 4 + 3x ^ 2 + 7x)/x (x ^ 4)/x + (3x ^ 3)/x + (7x)/L x ^ 3 + 3x ^ 2 + 7 Use the FOIL Method to simplify the following: (x - 3)(x - 4) x ^ 2 + 4x - 3x - 12 x ^ 2 + x - 121 (x - 7)(x - 6) x ^ 2 - 6x - 7x - 42 x ^ 2 - 13x - 42 (2x + 4)(2x + 3) 4x ^ 2 + 4x + 8x + 12 4x ^ 2 + 14x + 12 (3x - 1)(x + 5) 3x ^ 2 + 15x - x - 5 3x ^ 2 + 14x - 5 Multiply Binomials by Trinomials (x + 5)(x ^ 2 - 6x + 3) x ^ 3 - 6x ^ 2 + 3x + 5x ^ 2 - 30x + 15 x ^ 3 - x ^ 2 - 27x + 15 (2x - 3)(4x ^ 2 + 8x - 2) 8x ^ 3 + 16x ^ 2 - 4x - 12x ^ 2 - 24x + 6 8x ^ 3 + 4x ^ 2 - 28x + 6