P.3 Classifying, Adding, and Subtracting Polynomials

P.3
Classifying/Adding/Subtracting
Polynomials

Combining Like Terms

Number Talk

There is only one number in the
entire world that works when
plugged into the following
equation:

What is it?

Can you disprove the above
statement?

Multiple Select

For what number does x = x^2?

• 0

• 1

• -1

• None of these

Important Definitions

Polynomial- a mathematical expression with multiple terms

Term- an expression made up of coefficients, variables, and exponents (no +/-
signs)

Coefficient- the number before the variable

Degree- the highest exponent number of the polynomial

Classifying Polynomials

By Degree:

●0- Constant

●1- Linear

●2- Quadratic

●3- Cubic

By Term:

●1- Monomial

●2- Binomial

●3- Trinomial

Multiple Choice

Classify by number of terms:
3x³ – 6x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

Classify by degree of polynomial:
3x² – 8x + 1

• Constant

• Linear

• Quadratic

• Cubic

Multiple Choice

Classify by number of terms:
12

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Adding/Subtracting Polynomials

We add/subtract polynomials by adding/subtracting the coefficient of
like terms:

A “like term” is classified by two pieces of criteria:

●Same variable(s)

●Same degree

Multiple Choice

Simplify the expression: 2x + 1 + 7x 

• 10x

• 10

• 9x + 1

• 9 + 1x

Multiple Choice

Simplify the expression: 7v + 2 + 12 + 2v

• 23

• 23v

• 9 + 14v

• 9v + 14

Multiple Choice

Collect like terms: 
4y + 8d - 2y + 3d

• 11d + 6y

• 11d + 2y

• 6y + 5d

Multiple Choice

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

• 2x² + 3x +1

• -2x² - 11x -4

• 2x² + 5x -7

• -2x² + 11x -4

Multiple Choice

(4x³-5x²+3x)+(-2x³-x²+6x)

• 2x³-6x²-9x

• 2x³+6x²+9x

• -2x³-6x²+9x

• 2x³-6x²+9x

Multiple Choice

(5x⁴ - 4x³ - 2x² + x - 19) - (x⁴ + 5x³ + 8x² + x + 5)

• 4x⁴ - 9x³ - 10x² - 24

• 4x⁴ - 9x³ - 10x² - 2x - 24

• 4x⁴ - 9x³ - 10x² + 2x - 24

• -4x⁴ - 9x³ - 10x² - 24

Multiple Choice

Find the difference. 
(3- 2x + 2x²) - (4x -5 +3x²)

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Multiple Select

What two things should you look for with like terms?

• Same variable

• Same constant

• Same degree

• Same sign

• None of these