Adding and subtracting polynomials - Set 1
1. Let's practice adding and subtracting polynomials.
To add polynomials, you can group like terms horizontally or write them in column form,
aligning like terms vertically.
Like terms are monomial terms that are either identical or differ only in their coefficients, such
as 4y and -7y, or -8x2z and 3x2z.
2. Let's use the horizontal method first to add polynomials.
Find (3x2 + 5x - 7) + (-9x2 + 4x + 9).
First, group the like terms. Then add the coefficients of the like terms and add the constants.
(3x2 + 5x - 7) + (-9x2 + 4x + 9)
= [3x2 + (-9x2)] + (5x + 4x) + (-7 + 9)
= [3 + (-9)]x2 + (5 + 4)x + (-7 + 9)
= -6x2 + 9x + 2
So the sum is -6x2 + 9x + 2.
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Adding and subtracting polynomials - Set 1
3. Now let's use the horizontal method to find the difference of polynomials.
Find (6x2 - 4x - 7) - (-5x - 9x2 + 8).
First, use additive inverses to rewrite the subtraction as addition.
Next, group the like terms. Then add the coefficients of the like terms and add the constants.
(6x2 - 4x - 7) - (-5x - 9x2 + 8)
= (6x2 - 4x - 7) + [5x + 9x2 + (-8)]
= (6x2 + 9x2) + (-4x + 5x) + [-7 + (-8)]
= (6 + 9)x2 + (-4 + 5)x + [-7 + (-8)]
15x2 + 1x + (-15)
= 15x2 + x - 15
So the difference is 15x2 + x - 15.
4. Let's use the vertical method to add polynomials.
Find (x2 + 3x + 2) + (4x + 5x2 - 6).
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Adding and subtracting polynomials - Set 1
5. Now let's use the vertical method to subtract polynomials.
Find (6x2 - 5x + 4) - (-2x2 - 5x + 7).
First, align like terms in columns.
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Adding and subtracting polynomials - Set 1
Now, try to work through the next problems step by step.
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Adding and subtracting polynomials - Set 1
1. Look at this sum.
(6x2 - 7x + 5) + (5x2 + 6x - 7)
The first step in the horizontal method is to group like terms. Which is the correct way to group
like terms?
A (6x2 + 6x) + [-7x + (-7)] + (5 + 5x2)
B (6x2 + 5x2) + (-7x + 6x) + [5 + (-7)]
2. (6x2 - 7x + 5) + (5x2 + 6x - 7)
= (6x2 + 5x2) + (-7x + 6x) + [5 + (-7)]
What is the next step to add these polynomials?
A (6 + 5)x2 + (-7 + 6)x + [5 + (-7)]
B (6 - 5)x2 + (-7 - 6)x + [5 + (-7)]
3. (6x2 - 7x + 5) + (5x2 + 6x - 7)
= (6x2 + 5x2) + (-7x + 6x) + [5 + (-7)]
= (6 + 5)x2 + (-7 + 6)x + [5 + (-7)]
What is the sum?
A 11x2 - 13x - 12
B 11x2 - x - 2
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Adding and subtracting polynomials - Set 1
4. Look at this difference.
(6x2 + 4x - 8) - (-3x - 5x2 + 9)
The first step in the vertical method is to align the like terms. Which is the correct way to align
like terms?
A B 5. (6x2 + 4x - 8) - (-3x - 5x2 + 9)
A B Page 6 of 10
Adding and subtracting polynomials - Set 1
6. (6x2 + 4x - 8) - (-3x - 5x2 + 9)
What is the difference?
A 11x2 + 7x - 17
B x2 + x - 1
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Adding and subtracting polynomials - Set 1
Now, work these practice problems on your own.
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Adding and subtracting polynomials - Set 1
1. Find (4x2 - 5x + 3) + (3x2 - 8x - 2).
A B C D 7x2 - 13x + 1
12x2 - 40x - 6
7x4 - 13x2 + 1
12x4 - 40x2 - 6
2. Find (7x2 - 8x - 4) + (-3x2 - x + 11).
A B C D 4x2 - 9x + 7
10x4 - 7x2 - 15
4x4 - 9x2 + 7
10x2 - 7x - 15
3. Find (x2 - 9x + 4) + (-10x2 - 3x - 3).
A B C D -9x2 - 12x + 1
11x2 - 6x + 7
11x4 - 6x2 + 7
-9x4 - 12x2 + 1
4. Find (-8x2 + 6x - 3) + (-7x2 - 12x + 4).
A -15x2 - 6x + 1
B -x4 + 18x2 - 7
C -x2 + 18x - 7
D -15x4 - 6x2 + 1
5. Find (4x2 + 6x + 5) + (5x2 + 7x + 4).
A B C D 9x4 + 13x2 + 9
9x2 + 13x + 9
-x2 - x + 1
-x4 - x2 + 1
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Adding and subtracting polynomials - Set 1
6. Find (9x2 - 6x - 4) + (-6x2 + 10x + 4).
A B C D 3x4 + 4x2
3x2 + 4x
15x4 - 16x2 - 8
15x2 - 16x - 8
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