Operations with Polynomials Review

Standard Form

100

Rewrite in Standard Form:

2x³ + 17x² - 33 + 9x⁴

9x⁴ + 2x³ + 17x² - 33

200

Rewrite in Standard Form:

5a² - 6a - 6a⁴ - 6a⁹ - 5a⁷

-6a⁹ - 5a⁷ - 6a⁴ + 5a² - 6a

300

Rewrite in Standard Form:

-6a⁴ + 10a³ + 14a⁷ - 22a² + 33

14a⁷ - 6a⁴ + 10a³ -22a² +33

400

Combine like terms and write in Standard Form:

13k -10k³ + k +1 - 2k³ +9

-12k³ + 14k + 10

500

Combine like terms and write in Standard Form:

4x - 9x² + 4x³ - 5x⁴ +11 - 4x³ -3x² - 8x + 4x²

-5x⁴ - 8x² - 4x + 11

Adding Polynomials

100

Add the Polynomials:

(4x + 9) +(x - 4)

5x + 5

200

Add the polynomials:

(-3a - 2) + (7a + 5)

4a + 3

300

Add the polynomials:

(x² +3x + 5) + ( -x² +6x)

9x + 5

400

Add the polynomials:

(t² + 3t³ -3) + (2t² +7t -2t³) 

t³ +3t² +7t -3

500

Add the polynomials:

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

Subtracting Polynomials

100

Subtract the polynomials:

(g - 4) - (3g - 6)

-2g + 2

200

Subtract the polynomials:

(-5h - 2) - (7h +6)

-12h - 8

300

Subtract the polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

400

Subtract the Polynomials:

(k² + 6k³ -4) - (5k³ + 7k -3k²)

k³ + 4k² -7k -4

500

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

200

Multiply the Polynomials:

2r²(2r + 5r)

4r³+ 10r³ 

300

Multiply the Polynomials:

2m (m + 2)

2m² + 4m

400

Multiply the Polynomials:

(4n)(3n + 4mn)

12n² + 16mn²

500

Multiply and name the Polynomial

(d )(d² - 4d + 1)

d³ - 4d² + d

Cubic trinomial

Name Polynomials

100

5a² - 6a - 6a⁴ 

trinomial

200

1

monomial

300

4x - 9x² + 4x³  +11

4 term polynomial

400

-4x³ + 4x³ - 33 + 4 + 9x⁵

^{hint: look closely at the number of terms after combining like terms}

binomial

500

(4x + 9) +(x - 4 + y)

Hint: look closely at the terms after completing the computation

trinomial