Name:
Date:
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Topic: Adding & Subtracting Polynomials
Essential Question: How can you use monomials to form other large expressions?
Warm – Up:
Write an equation of the line that passes
through the given point and is perpendicular
to the graph of the given equation.
(3, 2);
- 3x + y = - 2
Flashback!!!
Do you remember what like terms are???
Copy down the following expressions and
circle the like terms.
1. 7x2 + 8x -2y + 8 – 6x
2. 3x – 2y + 4x2 – y
3. 6y + y2 – 3 + 2y2 – 4y3
Adding & Subtracting Polynomials
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Vocabulary:
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Monomial – is a real number, a variable, or a product of a
real number and one or more variables with whole-number
exponents.
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Ex: x, p, 4xy, 6, - 2r
Degree of Monomial – is the sum of the exponents of its
variables.
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Degree of the monomial = 6
Polynomial – is a monomial or a sum of
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Ex: 34p2q3r =
monomials.
Ex: 4x2 + 7x + 3 – 2y – 5xy
Degree of a Polynomial -
based on the degree of the
monomial with the greatest exponent.
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Ex: 4x2 + 7x + 3
Degree of the polynomial = 2
Solve the polynomials.
x2 + 4y + 3 + 2x and 3y + 5 + xy + x
1.
2.
3.
4.
x2 + 3x + 7y + xy + 8
x2 + 4y + 2x + 3
3x + 7y + 8
x2 + 11xy + 8
Adding Polynomials
Find the sum. Write the answer in standard format.
(5x 3 – x + 2 x 2 + 7) + (3x 2 + 7 – 4 x) + (4x 2 – 8 – x 3)
SOLUTION
Vertical format: Write each expression in standard form. Align like terms.
5x 3 + 2 x 2 – x + 7
3x 2 – 4 x + 7
3
2
+ – x + 4x
–8
4x 3 + 9x 2 – 5x + 6
Adding Polynomials
Find the sum. Write the answer in standard format.
(2 x 2 + x – 5) + (x + x 2 + 6)
SOLUTION
Horizontal format: Add like terms.
(2 x 2 + x – 5) + (x + x 2 + 6) = (2 x 2 + x 2) + (x + x) + (–5 + 6)
= 3x 2 + 2 x + 1
Add the following polynomials:
1. (9y - 7x + 15a) + (- 8a + 8x -3y )
2. (3a2 + 3ab - b2) + (4ab + 6b2)
3. (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)
Practice Time!
4. Find the sum.
(5a – 3b) + (6b + 2a)
a)
b)
c)
d)
3a – 9b
3a + 3b
7a + 3b
7a – 3b
Subtracting Polynomials
Find the difference.
(–2 x 3 + 5x 2 – x + 8) – (–4 x 3 + 3x – 4)
SOLUTION
Use a vertical format. To subtract, you add the opposite. This means you
multiply each term in the subtracted polynomial by –1 and add.
–2 x 3 + 5x 2 – x + 8
– –4 x 3
+ 3x – 4
No change
Add the opposite
–2 x 3 + 5x 2 – x + 8
+ 4 x3
– 3x + 4
Subtracting Polynomials
Find the difference.
(–2 x 3 + 5x 2 – x + 8) – (–4 x 2 + 3x – 4)
SOLUTION
Use a vertical format. To subtract, you add the opposite. This means you
multiply each term in the subtracted polynomial by –1 and add.
–2 x 3 + 5x 2 – x + 8
– –4 x 3
+ 3x – 4
–2 x 3 + 5x 2 – x + 8
+ 4 x3
– 3x + 4
2x 3 + 5x 2 – 4x + 12
Subtracting Polynomials
Find the difference.
(3x 2 – 5x + 3) – (2 x 2 – x – 4)
SOLUTION
Use a horizontal format.
(3x 2 – 5x + 3) – (2 x 2 – x – 4)
= (3x 2 – 5x + 3) + (– 2 x 2 + x + 4)
= (3x 2 – 2 x 2) + (– 5x + x) + (3 + 4)
= x 2 – 4x + 7
Subtract the following polynomials:
4. (15a + 9y - 7x) - (-3y + 8x - 8a)
5. (7a - 10b) - (3a + 4b)
6. (4x2 + 3y2 - 2xy) - (2y2 - xy - 3x2)
Find the difference.
(5a – 3b) – (2a + 6b)
a)
b)
c)
d)
3a – 9b
3a + 3b
7a + 3b
7a – 9b
Additional Practice:
Page 477 (1 - 4)
Page 478 (30, 32, 36, 43)
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Home-Learning #1:
Page 478 (38, 40, 43, 46, 53)