Polynomials Review

Definitions

100

Given: 

7x^5-14x^3+2x-9

What is the leading coefficient of the polynomial? 

7

200

Given: 

7x^5-14x^3+2x-9

What is the constant? 

-9

300

Given: 

5x^4+13x-3x^7-21+2x^6+4x^3

Rearrange the above polynomial in standard form. 

-3x^7+2x^6+5x^4+4x^3+13x-21

400

Given: 

8x^4-x^2+3x^6+4-5x

What is the degree of the polynomial above? 

6

500

Write the polynomial in standard form given the following: 

Leading coefficient = 3

Coefficients (in order) = 3, 1, -6

Degree = 3

Constant = -2

3x^3+x^2-6x-2

Combining Like Terms

100

Solve: 

y+y

2y

200

Solve: 

(5a-8b)+(4b-5a)

-4b

300

Solve: 

(4x-7y+3z)+(x+6y-5z)

5x-y-2z

400

Solve: 

(a+4b)+(6b-6a)

** Write your answer in standard form

-5a+10b

500

Solve: 

(m+n-10)+(5n+3)+(-8n+2m)

** Write the polynomial in standard form

3m-2n-7

Distribution

100

Solve: 

2(3x-6y)

6x-12y

200

Solve: 

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

-12x^2+20x-4

300

Solve: 

x(x+9)

x^2+9x

400

Solve: 

5x(2x^2-x+10)

10x^3-5x^2+50x

500

Solve:

2x^3(x^7-2x^4+3x^3-5)

2x^10-4x^7+6x^6-10x^3

Distribution + Combining Like Terms

100

Solve: 

(x+y)+3(4x+2y)

13x+7y

200

Solve: 

2(3a+5b)-4(2a-2b)

-2a+18b

300

Solve: 

3(x^2-x+1)+x^2(x^2-4x+7)

x^4-4x^3+10x^2-3x+3

400

Solve: 

x^3(3x^2-4x)-x(7x+8)

3x^5-4x^4-7x^2-8x

500

Solve: 

2x^2(4x^2+8x-12)-4x^3(3x-8)

-4x^4+48x^3-24x^2