Chapter 5 Part 1 Review

Determining Degree

100

3x⁴

4^th Degree Polynomial

200

What is the degree of the following polynomial: 

x³-2x²-x+1

3rd Degree Polynomial

300

(x⁴+x³+x⁵)-(x⁴+x⁵)-(x³-x²)

2^nd Degree Polynomial

400

Determine the Degree of the following Polynomial:

x^-2+x^-1-x^-3

This is not a polynomial, so it has no degree.

500

What is the degree of the following Polynomial:

(x²-2)(x-3)³(x+3)

6^th degree polynomial

Polynomial Addition

100

(2x + 5y) + (3x – 2y)

5x-3y

200

(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

4x³+x²-3x+1

300

(7x² – x  – 4) + (x² – 2x – 3) + (–2x² + 3x + 5)

6x²-2

400

(x³ + 5x² – 2x) + (x³ + 3x – 6) + (–2x² + x – 2)

2x³ + 3x² + 2x – 8

500

(3x² – 5x – 1) – (x³ – 2x² + 4) + (9x³ + 5x² – 3x – 2)

8x³ + 10x² – 8x + 1

Polynomial Subtraction

100

8x²-3x²

5x²

200

-2a²b³-(-5a²b³)

3a²b³

300

(8x³y+2x²y)-(2x³y-3x²y)

6x³y+5x²y

400

-2(3a³+a²)-5(2a³-a²+a)

-16a³+3a²-5a

500

(17x⁴-3x²-65x-12)-(23x⁴+14x²+3x-23)

-6x⁴+17x²-68x+11

Multiplying/Factoring GCF

100

Multiply the following: 

(3x+y)(3x-y)

9x²-6xy-3y²

200

Multiply the following: 

(x+2)²

x²+4x+4

300

Factor the following: 

-18a²b-12ab²

-6ab(3a+2b)

400

Factor the following:

12a⁶b⁴c²+15a²b⁴c⁶

3a²b⁴c²(4a⁴+5c⁴)

500

Factor the following: 

(x+y)³+(x+y)

(x+y)((x+y)²+1)

Factoring by Grouping

100

2c+2d-cd-d²

(c+d)(2-d)

200

3c-cd+3d-c²

(3-c)(c+d)

300

ab-b²-bc+ac-bc-c²

(b+c)(a-b-c)

400

2n⁴p-2n²-n³p²+np+2mn³p-2mn

n(2n-p+2m)(n²p-1)

500

7u+v²-7v-uv

(v-u)(v-7)