Operations on Polynomials

Degree/Lead. Coeff.

100

Name the degree and the leading coefficient of the following:

-6v⁶

Degree: 6

Leading Coefficient: -6

200

Name the degree and the leading coefficient of the following:

-9n⁵-5n⁴

Degree: 5 

Leading Coefficient: -9

300

Name the degree and the leading coefficient of the following:

3

Degree: 0

Leading Coefficient: 3

400

Name the degree and the leading coefficient of the following:

7r-9r²

Degree: 2

Leading Coefficient: -9

500

Name the degree and the leading coefficient of the following:

10-3k-9k⁶

Degree: 6

Leading Coefficient -9

Name of Polynomials

100

Give the name of the polynomial based on the number of terms:

10n⁶

Monomial

200

Give the name of the polynomial based on the number of terms:

8x²-3x+5

Trinomial

300

Give the name of the polynomial based on the number of terms:

-10+3p

Binomial

400

Give the name of the polynomial based on the number of terms:

6x²-6x²+8x-2

Binomial

500

Give the name of the polynomial based on the number of terms:

7m⁵-6-3n⁴+5m

4-Term Polynomial

Adding Polynomials

100

Simplify:

(6n³+4n⁴)+(4n³+4n⁴)

8n⁴+10n³

200

Simplify:

(7-3m²)+(5m²+5m-1)

2m²+5m+6

300

Simplify:

(1+5v²+3v)+(8v+6-6v²)

v²+11v+7

400

Simplify:

(3-7p+p³+8p²)+(4+8p²-p+4p³)+(4p²+p³)

6p³+20p²-8p+7

500

Simplify:

(n⁴+8n³+6n+3)+(5n⁴-5-6n+2n²)+(6n⁴+3-6n-8n³)

12n⁴+2n²-6n+1

Subtracting Polynomials

100

Simplify:

(8a²-6a)-(6a²-8a)

2a²+2a

200

Simplify:

(7n²-6)-(7+6n²-2n³)

2n³+n²-13

300

Simplify:

(8x+5x²+4)-(5+2x²+8x³)

-8x³+3x²+8x-1

400

Simplify:

(r⁴+6+4r-2r³)-(6r⁴-2r+7r²-r³)

-5r⁴-r³-7r²+6r+6

500

Simplify:

(3r+1-3r²+4r⁴)-(8r²-3-r⁴+r)-(5r-8r⁴-3-7r²)

13r⁴-4r²-3r+7

Multiplying Polynomials

100

Simplify:

2n³(7n-1)

14n⁴-2n³

200

Simplify:

7r²(-r²-5r+5)

-7r⁴-35r³+35r²

300

Simplify:

(2r-6)(4r+7)

8r²-10r-42

400

Simplify:

(4v-6)(3v²-7v+8)

12v³-46v²+74v-48

500

Simplify:

(4n²-2n+8)(5n²+4n+8)

20n⁴+6n³+64n²+16n+64