Polynomials

Classifying Polynomials(:

100

Has just one term. 

Example: 4x²

Monomial

200

Has two terms.

Example: 5x³-4x

Binomial

300

Has three terms.

Example: 3y² + 5y -2

Trinomial

400

Classify this polynomial by the number of terms.

3x⁵ - 3x + 78

Trinomial

500

Classify this polynomial by the number of terms and identify the degree.

7yz⁴ + 3x⁵ + 5y² + 6zyx⁸ + 8z

polynomial with 5 terms.

degree of the polynomial is 10

Adding with Single Variables

100

(14 + 9k) + (–14 – 7k)

2k

200

(16 + 4r² + 5r³) + (3r³ + 2r²)

8r³ + 6r² + 16

300

(–6x⁷ + 10 + 3x⁵) + (15 – 2x⁵ – 9x)

-5x⁷ + x⁵ - 9x + 25

400

Add the polynomial then classify.

(–2y + 7y⁴+ 5y⁵ – 4y² – 2y⁶) + (y + 9y⁶ + 6y² )

7y⁶ + 5y⁵ +7y⁴ +2y² - y

polynomial with 5 terms

500

Add the following polynomial then classify the polynomial and find the degree.

(2n – 7n⁵) + (6n³ + 4n² + 5n⁵ – 13 – 2n)

–2n⁵ + 6n³ + 4n² – 13

Polynomial with 4 terms

Degree: 5

Subtracting with Single Variables

100

(8s² + 6s + 5) – (s² + s)

7s² + 5s + 5

200

(2x² + 3x + 15) – (–x³ + 7x)

x³ + 2x² – 4x + 15

300

(–m⁷ + 9m³ + 5m) – (–m⁷ + 9m³ – 4m)

9m

400

Add the polynomial and then classify.

(5p⁶ + 6p² + p) – (8p⁶ + 10p³ + 2p)

–3p⁶ – 10p³ + 6p² – p

polynomial with 4 terms 

500

Add the following polynomial then classify the polynomial and find the degree.

(10v⁶ + 7v⁴ – 5v³ + 3v² + 16) – (v⁶ + 2v⁴)

9v⁶ + 5v⁴– 5v³ + 3v² + 16

Polynomial with 5 terms

Degree: 6

Adding with Multi Variables

100

(mn³ + 3) + (m² – 1)

mn³ + m² + 2

200

(t⁵ + 10rs) + (–3r – 2t⁵⁾

–t⁵ + 10rs – 3r

300

 (3zy⁴-2y²+6rs-8)+(zy⁴-3y³+4y²-8rs+3)

4zy⁴-3y³+2y²-2rs-5

400

Add the polynomial and then classify.

(2x² + 3mn + 2) + (3x² - 5mn -1)

5x² - 2mn + 1

Trinomial

500

Add the following polynomial then classify the polynomial and find the degree.

(3qr⁴s² + 6) + (–10 + rs + qr⁴ s² )

4qr⁴s²+ rs – 4

Trinomial 

Degree: 7

Subtracting with Multi Variables

100

(2mn + 4m) - (2mn - 6m) =

10m

200

(-s² - 3) - (2s² + 10sq)=

*remember to change signs*

= -3s² - 10sq - 3

300

(6x³yz- 4yx² + x - 9) - (3yx² + 7x + 3) =

*remember to change signs*

6x³yz- 7yx² - 6x - 12

400

Subtract yz⁵ - xy^4z from y² + 3y^4.

Set up: (y² + 3xy⁴z) - (yz⁵ - y⁴)

Answer: y² + 2xy⁴z - yz⁵

500

Subtract t⁴ - 3t² + 7 from 5t³ - 9 then classify the polynomial and find the degree.

Set up: (5t³ - 9) - (t⁴ - 3t² + 7) =

Answer: 

-t⁴ + 5t³ + 3t² - 16

Polynomial with 4 terms

Degree: 4