Polynomial - Review

Definitions

100

What is a number or variable separated by a plus or minus?

A term

200

The number in front of a variable is called

A coefficiant

300

A term with no variables is called

Constant

400

The highest exponent of a polynomial is called

The degree

500

Terms with the same variables and degrees are called 

Like/common terms

Addition

100

Add

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

5x + 5

200

Add

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

4a + 3

300

Add

(x² +3x + 5) + ( -x² +6x)

9x + 5

400

Add

(t² + 3t³ -3) + (2t² +7t -2t³) 

t³ +3t² +7t -3

500

A rectangle has a length of (1 -2x + 2x²) and a width of (-1 + x² + 2x), determine the perimeter.

6x²

Subtraction

100

Subtract

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

-2g + 2

200

Subtract

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

-12h - 8

300

Subtract

(-x² - 5) - (-3x² -x -8)

2x² + x +3

400

Subtract

(k² + 6k³ -4) - (5k³ + 7k -3k²)

k³ + 4k² -7k -4

500

A rectangle has a perimeter of (12x² - 8x) and a length of (2x² + x). Determine the width of the rectangle

4x² - 5x 

Multiplication

100

3(3x)

9x

200

(3xz³)(-2xyz)

-6x²yz⁴

300

Multiply

3x² (2x⁴ + 4)

6x⁶ + 12x²

400

(4x)(4x-3)

16x²-12x

500

A rectangle has a length of (2x-3y+6) and a width of (3y), determine its area.

6xy-9y²+18y

Division

100

(2x+6)/2

x+3

200

(4x³ + 16x² - 20x)/4x

x²+4x-5

300

6x²/x

6x

400

The area of a rectangle is 6x²+24x. One of its sides has a length of 6x. What is the width of the rectangle?

x+4

500

(5xy²-10x²y-30xy)/5xy

y²-2x-6