8.1 Adding and Subtracting Polynomials

8.1 Adding and Subtracting Polynomials

Two monomials

x+y

3-a²

2x+4y​

​Binomial:

​Monomial:

Fractions are NOT monomials!

​Trinomial:

Three monomials

x+y+z

3+a-b

2x²-4y​+5z

​Polynomial:

the highest power of a variable in a polynomial expression

​

Degree

Multiple Choice

$$4y-5xz$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$x^3-10x+1$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$5x$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$-6.5$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$6x^3+4x+y+3$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$-3y^2-2y+4y-1$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

​-3y² - 2y + 4y - 1

We need to simplify first!

-3y² + 2y - 1​

Always simplify as much as possible (remember like terms)

9+5x²+x⁴-3x³+x-2x⁶

Put this polynomial in standard form:

​4x⁴+2x+3

Standard Form: terms in order from greatest to least degree

​3y³-y²+12y

​y⁸+8y³+2y²-y+7

(2x²+5x-7) + (3-4x²+6x)

Combine like terms!​

Add Polynomials

(3y+y³-5) + (4y²-4y+2y³+8)​

Line up like terms and combine!

Add Polynomials

Multiple Choice

$$\left(5x^2-3x+4\right)+\left(6x-3x^2-3\right)$$  

• $$11x^2+1$$  

• $$8x^2+3x-1$$  

• $$2x^2+3x+1$$  

• $$6x^2+1$$  

(3-2x+2x²) - (4x-5+3x²)

Subtract by adding the inverse.

Subtract Polynomials

(7p+4p³-8) - (3p³+2-9p)

Line up like terms and combine!​

Subtract Polynomials

Multiple Choice

$$\left(4x^3-3x^2+6x-4\right)-\left(-2x^3+x^2-2\right)$$  

• $$2x^3-2x^2+6x-2$$  

• $$2x^3-2x^2-6$$  

• $$6x^3-4x^2-6$$  

• $$6x^3-4x^2+6x-2$$  

Multiple Choice

What is the degree of the polynomial? 5x⁵ - 6x⁶ + 2

• 1

• 5

• 6

• 11

Multiple Choice

Add the polynomials.
(2x + 5y) + (3x - 2y)

• 3x + 5y
• 5x + 3y
• 5x + 7y
• 7xy + 1xy

Multiple Choice

What is the standard form of the polynomial,

9x² + 5x + 27 + 2x³

• 27 + 5x + 9x² + 2x³

• 9x² + 5x + 2x³ + 27

• 9x² + 5x + 27 + 2x³

• 2x³ + 9x² + 5x + 27

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 Choice

What are like terms?

• The same coefficients.

• The same variables with different exponents.

• Terms with the same variable and exponents combination.

• Different variables with same exponents.