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Pre-Algebra - Polynomials: Add and Subtract

This Math quiz is called 'Pre-Algebra - Polynomials: Add and Subtract' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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A polynomial is two or more monomial numbers that are linked together in an equation by an addition sign (+), subtraction sign (-) or a multiplication sign (x). For example: 3x8 + 5x5 + 2x3 + x. This example has four monomials that are linked by addition signs (+) making it a polynomial.

1.
(20x5 + x + 19) + (13x4 + 7x - 24)
33x9 + 8x - 5
20x5 + 13x4 + 8x + 5
33x9 + 8x2 - 5
20x5 + 13x4 + 8x - 5
(20x5 + x + 19) + (13x4 + 7x - 24)
20x5
13x4
x + 7x = 8x
19 - 24 = -5
Solution: 20x5 + 13x4 + 8x - 5
Answer (d) is the correct solution
2.
(22x5 + 16x4 + 11x - 31) + (8x4 + 9x2 + 35x + 42)
30x5 + 24x4 + 9x2 + 46x + 11
22x5 + 24x4 + 9x2 + 46x + 11
30x9 + 24x8 + 9x2 + 46x + 11
22x5 + 8x4 + 9x2 + 46x + 11
(22x5 + 16x4 + 11x - 31) + (8x4 + 9x2 + 35x + 42)
22x5
16x4 + 8x4 = 24x4
9x2
11x + 35x = 46x
-31 + 42 = 11
Solution: 22x5 + 24x4 + 9x2 + 46x + 11
Answer (b) is the correct solution
3.
(48x6 + 32x3 + 22) - (9x6 + 16x3 - 4)
39x6 + 16x3 + 18
39x6 + 16x3 + 26
57x6 + 48x3 + 18
57x6 + 16x3 + 26
(48x6 + 32x3 + 22) - (9x6 + 16x3 - 4)
(48x6 + 32x3 + 22) + (-9x6 - 16x3 + 4)
48x6 - 9x6 = 39x6
32x3 - 16x3 = 16x3
22 + 4 = 26
Solution: 39x6 + 16x3 + 26
Answer (b) is the correct solution
4.
(7x6 + 3x4 - 5x2 + 23) + (5x6 + 4x2 - 14x + 33)
12x6 + 3x4 + 9x2 - 14x + 56
12x6 + 3x4 - x2 + 56
12x6 + 3x4 - x2 - 14x + 56
12x6 + 3x4 - x2 - 14x - 10
(7x6 + 3x4 - 5x2 + 23) + (5x6 + 4x2 - 14x + 33)
7x6 + 5x6 = 12x6
3x4
-5x2 + 4x2 = -x2
-14x
23 + 33 = 56
Solution: 12x6 + 3x4 - x2 - 14x + 56
Answer (c) is the correct solution
5.
(4x5 - 6x2 + 27) - (-13x5 + 2x2 + 20)
-9x5 - 4x2 + 47
17x5 - 4x2 + 47
17x5 - 8x2 + 7
9x5 + 4x2 + 7
(4x5 - 6x2 + 27) - (-13x5 + 2x2 + 20)
(4x5 - 6x2 + 27) + (13x5 - 2x2 - 20)
4x5 + 13x5 = 17x5
-6x2 - 2x2 = -8x2
27 - 20 = 7
Solution: 17x5 - 8x2 + 7
Answer (c) is the correct solution
6.
(12x4 + 9x - 15) - (6x4 + 8x - 10)
18x4 + 17x - 25
6x4 + x - 5
6x4 + 17x - 25
18x4 + x + 5
(12x4 + 9x - 15) - (6x4 + 8x - 10)
(12x4 + 9x - 15) + (-6x4 - 8x + 10)
12x4 - 6x4 = 6x4
9x - 8x = x
-15 + 10 = -5
Solution: 6x4 + x - 5
Answer (b) is the correct solution
7.
(-6x2 + 7x - 9) + (6x2 - 5x + 13)
x2 + 2x + 4
x2 + 2x + 22
2x + 4
x2 + 12x + 22
(-6x2 + 7x - 9) + (6x2 - 5x + 13)
7x - 5x = 2x
-9 + 13 = 4
Solution: 2x + 4
Answer (c) is the correct solution. [Note: As (-6x and 6x cancel each other out, they do not need to appear in the solution.]
8.
(9x6 + 5x4 - 3x2 + 4) - (-2x6 + 7x4 - 12x + 99)
11x6 - 2x4 - 3x2 + 12x - 95
7x6 - 12x4 + 9x - 103
7x6 - 2x4 + 9x - 95
11x6 + 2x4 + 12x - 95
(9x6 + 5x4 - 3x2 + 4) - (-2x6 + 7x4 - 12x + 99)
(9x6 + 5x4 - 3x2 + 4) + (2x6 - 7x4 + 12x - 99)
9x6 + 2x6 = 11x6
5x4 - 7x4 = -2x4
-3x2
12x
4 - 99 = -95
Solution: 11x6 - 2x4 - 3x2 + 12x - 95
Answer (a) is the correct solution
9.
(4x3 + 2x2 - 6x + 18) - (-2x3 + 3x2 - 39x - 16)
6x3 - x2 + 33x + 34
2x3 + 5x2 - 33x + 2
6x3 - 5x2 + 33x + 34
2x3 - x2 - 33x + 34
(4x3 + 2x2 - 6x + 18) - (-2x3 + 3x2 - 39x - 16)
(4x3 + 2x2 - 6x + 18) + (2x3 - 3x2 + 39x + 16)
4x3 + 2x3 = 6x3
2x2 - 3x2 = -x2
-6x + 39x = 33x
18 + 16 = 34
Solution: 6x3 - x2 + 33x + 34
Answer (a) is the correct solution
10.
(9x7 + 2x4 + 44) + (67x7 + 51x4 + 1)
76x7 + 53x4 + 43
76x7 + 49x4 + 45
76x14 + 53x8 + 45
76x7 + 53x4 + 45
(9x7 + 2x4 + 44) + (67x7 + 51x4 + 1)
9x7 + 67x7 = 76x7
2x4 + 51x4 = 53x4
44 + 1 = 45
Solution: 76x7 + 53x4 + 45
Answer (d) is the correct solution
Author:  Christine G. Broome