Operations of Polynomials

Addition

100

(4x) + (2x + 1)

6x +1

200

(t² - 3t) + (2t -1 )

t²+t -1

300

 ( 4x -5 ) + ( 3x^{3  _} x )

 3x³ +3x - 5 

400

( 1/4x⁴ + 2/5x² -8x ) + ( 3x² - 5x +2/9 )

1/4x⁴ +17/5x² - 13x +2/9

500

(1/3x⁴ + 2/3 x³ - 1/5x² + 3/7x -1 ) + (2/7x⁴ - 2/4x³ - 4/5x² +1/7x +4 )

13/21x⁴ -1/6x³ -1x² +4/7x +3

Subtraction

100

( 2x² +8 ) - ( x² +2)

x² +6

200

(3n +4 ) - (n³ +3n)

-n³ +4

300

(x +2) - (-2x² +4)

2x² +x -2

400

(1/2x -2 ) - ( 3/4x +2/5 )

-1/4x - 12/5 

500

(3/7x³ - 7/2 x² +2/3)- (6 x² + x +5/4) 

3/7x³ -19/2 x² -1x -7/4

Multiplication

100

x * x 

x²

200

(3x + 5 ) * (4x -6 )

12x² +2x-30

300

(3x³ -4x² +2x -1) * x

3x⁴ -4x³ +2x² -1x

400

(3x³ -4x² +2x -1 ) *( x + 3 )

3x⁴ +5x³ -10x² +5x -3 

500

( 2/3x³ -5x² +4/3 ) *( 1/7x³ -3/2x² +3 )

2/12x⁶ -12/7x⁵ +15/2x⁴ +46/21x³-17x² +4

Vocabulary

100

A term with no variable 

Constant 

200

A function with the highest degree (exponent) of 1

A function with the highest degree (exponent) of 2

Linear and Quadratic 

300

A polynomial with two terms 

A polynomial with three terms

Binomial

Trinomial 

400

4x + 2 

Has the highest degree of what?

Has how many terms?

Linear binomial

500

4x² + 2x +2 

Has the highest degree of what?

Has how many terms?

Quadratic Trinomial

Factor Review

100

x² +10x

x (x+10)

200

(n² -25)

(n+5)(n+5)

300

m³ +13m²+36m

m (m+9)(m+4)

400

3r⁴-36r³ +96r²

3r² (r -8)(r-4)

500

30r² -276r +288

6 (5r -6)(r-8)