Polynomial Operations

Classifying Polynomials

100

Determine the degree of the following polynomial:

-3x^2+5x-1

Degree: 2

200

Is the following polynomial a monomial, binomial, or trinomial?

2x-3x^2

Binomial

300

Classify the polynomial by its degree and the number of terms:

-4x^4+3x^2-x

Quartic Trinomial

400

Classify the polynomial by its degree and the number of terms:

3x^2-x

Quadratic binomial

500

Classify the polynomial by its degree and the number of terms:

-2x^3-3x^2+1

Cubic Polynomial with 4 Terms

Adding Polynomials

100

Add the following polynomials. Write your final answer in standard form.

(4x^2+4)+(19x^2-7)

23x^2-3

200

Add the following polynomials. Write your final answer in standard form.

(13x^2-2x+1)+(9x^2-7)

22x^2-2x-6

300

Add the following polynomials. Write your final answer in standard form.

(-x^3+8x^2-5)+(10x^3-x^2+1)

9x^3+7x^2-4

400

How do you add polynomials?

Combine like terms

500

Add the following polynomials. Write your final answer in standard form.

(-4x^3+6x^2+8)+(10x^3-3)

6x^3+6x^2+5

Subtracting Polynomials

100

Subtract the following polynomials. Write your final answer in standard form.

(3x+2)-(11x-6)

-8x+8

200

Subtract the following polynomials. Write your final answer in standard form.

(5x^2+2x-3)-(8x+6)

5x^2-6x-9

300

Subtract the following polynomials. Write your final answer in standard form.

(-4x^2-3x+9)-(-2x^2-5)

-2x^2-3x+14

400

What is the first step when subtracting polynomials?

Distribute the negative.

500

Subtract the following polynomials. Write your final answer in standard form.

(x^2-x+4)-(x^2+x-2)

-2x+6

Multiplying Polynomials

100

Multiply the polynomials. Write your final answer in standard form.

-3x(2x^2+4)

-6x^3-12x

200

Multiply the polynomials. Write your final answer in standard form.

(9x+1)(6x+2)

54x^2+24x+2

300

Multiply the polynomials. Write your final answer in standard form.

(7x+4)(7x-4)

49x^2-16

400

What do you draw when multiplying polynomials?

The box method.

500

Multiply the polynomials. Write your final answer in standard form.

(2x-5)(3x^2-x+6)

6x^3-17x^2+17x-30

Dividing Polynomials

100

Divide the following polynomials. Write your final answer in standard form.

(x^2+5x+6)÷(x+2)

x+3

200

Divide the following polynomials. Write your final answer in standard form.

(2x^3+3x^2-5x+4)÷(x-1)

x+7+30/(x-4)

300

Divide the following polynomials. Write your final answer in standard form.

(x^2+3x+2)÷(x-4)

2x^2+5x+0+4/(x-1)

400

How do you know if something is a factor of a polynomial?

If the remainder is zero, it is a factor.

500

Divide the following polynomials. Write your final answer in standard form.

(x^3-9x+8)÷(x-2)

x^2+2x-5+(-2)/(x-2)