Adding, Subtracting and Multiplying Polynomials

Adding, Subtracting and Multiplying Polynomials

So, Combining like terms:

• If adding like terms, underline the like terms and then combine them by adding or subtracting the exponents

• If subtracting like terms, change the signs of each term behind the parenthesis. Next, find the like terms. Combine the like terms to simplify the expressions.

Multiple Choice

Combine Like Terms:
4y + 3x³ + 2y + 8x³ - 6y

• 11x³
• 11x³ + 12y
• 5x³
• 11x⁶

Multiple Choice

Add the following polynomials:

(x³ + 6x - 5) + (-6x² + 4x + 3)

• x³ - 6x² +10x - 8

• x³ - 6x² +10x + 2

• x³ - 6x² +10x - 2

• x³ + 4x - 2

Multiple Choice

Determine the degree of the following polynomial:

x⁴ - 9x + 1

• 1

• 4

• 5

• -9

Multiple Choice

Name the following polynomial using the degree and number of terms. 
15x³ + 6 

• Cubic Binomial
• Linear Binomial
• Cubic Trinomial
• Cubic Monomial

Multiple Choice

How many terms are in the following polynomial?
3x³ - 2x + 8x -16

• -16
• 2
• 3
• 8

Multiple Choice

Simplify the expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3 
• -7n² - 8n + 3 
• -6n² - 8n + 3
• -7n² - 4n + 3

Multiple Choice

(4x²+ x) - (x²+ 2x)

• 3x² - x
• 4x² + 2x
• 3x² + 3x
• 3x² + 2x

Multiple Choice

What is the the standard form for the following expression?

-6x + 4x² - 13

• -13 - 6x + 4x²

• 4x²-6x - 13

• -13 + 4x² - 6x

• 4x² - 13 - 6x

Multiple Choice

What is the the standard form for the following expression?

-6x + 4x² - 13

• -13 - 6x + 4x²

• 4x²-6x - 13

• -13 + 4x² - 6x

• 4x² - 13 - 6x

Use the distributive property

• When multiplying polynomials... multiply the coefficients, add the exponents. 3x^2 * 2x so 3 x 2 =6 and x^2 * x is x^3

• so 6x^3

Multiple Choice

Multiply the following polynomial by the monomial:

3x(4x² - x - 3)

• 12x² - 3x - 9

• 7x³ - 3x² - 6x

• 12x³ - 3x² - 9x

• 12x³ - 3x² - 6

Multiple Choice

-5x⁶(3x² - 12x + 30)

• -15x⁸ + 60x⁷ - 150x⁶
• 15x⁸ - 60x⁷ - 150x⁶
• 8x⁶ - 17x + 35
• -8x⁶ + 17x - 35x²

Multiple Choice

Simplify:

5(3x+2)

• 3x+10

• 15x+10

• 15x-10

• 3x-10

Multiple Choice

(x-3)(x²+2x+7)

• x³-x²+x-21
• x³+5x+13x-21
• x³-3x²+7x-21
• x²+2x-3

Multiple Choice

 Multiply: (r + 7)(r − 7) 

• r ² − 49 
• r ² + 14
• r ² − 7r + 49 

Multiple Choice

Multiply (3x – 1)(x + 5) 

• 3x² + 4x + 5
• 3x² + 4x - 5
• 3x² + 14x + 5
• 3x² + 14x - 5

Multiple Choice

Simplify the product.

(2x – 6)²

• 4x² – 24x + 36
• 4x² – 8x + 36
• 4x² + 36
• 4x² – 12x + 36

Multiple Choice

(4x+1)(5x−2)

• 20x² + 3x − 2

• 20x² − 11x + 5

• 20x² − 18x + 2

• 20x² − 3x − 2

Multiple Choice

(4x+1)(5x−2)

• 20x² + 3x − 2

• 20x² − 11x + 5

• 20x² − 18x + 2

• 20x² − 3x − 2