Polynomial Math

Definitions

100

What is a number or variable in a polynomial that is separated  by an addition or subtraction sign

a term

200

The number before a variable within a term is called the...

Coefficient

300

A term that has no variable

Constant

400

The highest exponent on the variables in a term

Degree of the term

500

Terms that have the same variables and the same degree are....

Like terms

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:

(2x² - 3x) - (x² -2x + 4)

x² + x - 4

Multiplying Polynomials

100

3(3x)

9x

200

Multiply the Polynomials:

(3x)(2y)

6xy

300

Multiply the Polynomials:

3x² (2x⁴ + 4)

6x⁶ + 12x²

400

(4x)(4x-3)

16x²-12x

500

(2x-3y+6)(3y)

6xy-9y²+18y

Dividing Monomials and Polynomials

100

Divide.

x² / x² 

x^2-2 = x⁰= 1

What is 1?

200

Divide without converting from scientific notation.

12b⁶

/

4b²

12/4 = 3

b^6-2 = 4

What is 3b⁴ ?

300

Divide without converting from scientific notation.

(2.25×10⁹)

/

(1.5×10⁶)

2.25/1.5 = 1.5

10^9-6 = 10³

What is 1.5 x 10³ ?

400

Find the quotient.

(10x³-8x²+4x-2)

/

2x

10x³/2x =5x² 

-8x²/2x = - 4x 

+4x/2x = + 2

-2/2x = - 1/x

What is 5x² - 4x + 2 - 1/x ?

500

Find the quotient

(8x²+6x+3) / (4x+1)

Divide using long division.

What is 2x+1 ?