Adding and Subtracting Polynomials

Adding and Subtracting Polynomials!🌟

Review from Yesterday: Polynomials

Multiple Choice

What kind of polynomial is this?

$$x^2+3x^5+9$$  

• monomial

• binomial

• trinomial

Multiple Choice

What is the degree of this polynomial?

$$x^5+4x^7+x$$  

• 1

• 5

• 7

• 13

• 12

Multiple Choice

What is the leading coefficient of this polynomial?

$$x^5+3x^7+x+4$$  

• 1

• 5

• 3

• 6

• 4

Adding Polynomials

1. Place like terms together
2. Add the like terms

Example: Adding Polynomials

Multiple Choice

Add the polynomials (x-2) and (x²+3)

• x²+x+1
• x³+5
• x³+1
• x³-1

Multiple Choice

Add these polynomials:

(5x + 2) + (4x + 5)

• 9x -7

• -9x-11

• 9x+7

• x+7

Multiple Choice

(2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

Subtracting Polynomials

To subtract Polynomials, first reverse the sign of each term we are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.

OR

Use distributive property with negative one on the second polynomial, then combine like terms.

Subtracting Polynomials Example

Multiple Choice

Subtract these polynomials:

(4x²+ x) - (x²+ 2x)

• 3x² - x

• 4x² + 2x

• 3x² + 3x

• 3x² + 2x

Multiple Choice

Subtract these polynomials:

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3

• -7n² - 8n + 3

• -6n² - 8n + 3

• -7n² - 4n + 3

Multiple Choice

Subtract these polynomials:

(x⁵ + x³) - (6x - x³ + 6x⁵)

• -5x⁵ + 2x³ - 6x

• 7x⁵ - 6x

• -5x³ + 2x² - 6x

• -5x⁵ - 6x

Make sure all the notes are in your notebook, and you are free to go!

-Ms. C