Alg. 1 8-1

8-1 Adding and
Subtracting
Polynomials

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Vocabulary

●
Polynomial: A monomial or the sum of
monomials

●Monomial: One part only

●Binomial: The sum of two monomials

●Trinomial: The sum of three monomials

Multiple Choice

Classify:
2x⁴+14x³−2x²

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

Classify:
2n³

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

How many Harry Potter books are there?

• 4

• 7

• 8

• 11

Multiple Choice

Classify:
x³ + 3x

• Monomial
• Binomial
• Trinomial
• Polynomial

Degrees

●Degree of a Monomial: To find the
degree of a monomial, add all the
exponents in the variables

●Degree of a Polynomial: The highest
exponent/power of any term in the
polynomial

Multiple Choice

Classify by the DEGREE:
2x² - 5

• 1
• 2
• 3
• 4

Find the degree of the polynomial

Example 1

Find the degree of the polynomial

Example 2

Poll

Would You Rather...

• have a job that you hate, but that pays you millions of dollars a year

• have a job that you love that pays you just enough to get by

Multiple Choice

What is the highest degree among terms in this polynomial?

6x² + 7x⁴ + x3 + x

• 1

• 2

• 3

• 4

What makes like terms

How do you combine them

Like Terms and Combining Them

1.

Same variable

2.

Same power/exponent

When you combine like
terms, you only combine
the COEFFICIENTS, the
big number, and powers
stay the same

●Find the sum

Example 3

●Find the sum

Example 4

Multiple Choice

Simplify by combining like terms

3x-5x

• 2x
• 8x
• -2x
• 15x²

Multiple Choice

Simplify by combining like terms

10x²+9x-5+3x²-8x-7

• 13x²+17x+12
• 14x²-12
• 13x²+x-12
• 2x²

Multiple Choice

What is the perimeter of the rectangle?

• x²+8x-5

• 2x²+16x-10

• 2x²+10x-8

• 6x-2

●Find the difference

Example 5

●Find the difference

Example 6

Multiple Choice

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2 
• x + 2
• 2x² + x - 10 
• x - 10 

Multiple Choice

Subtract the following polynomials:

$$(6x^2+10x-9)-(4x^2-13)$$

• $$2x^2+10x-22$$

• $$10x^2+10x-22$$

• $$2x^2+10x-4$$

• $$2x^2+10x+4$$