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

The number in front of the term with the highest exponent.  

Leading Coefficient

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(x-2)^2

4x^3-16x^2+16x

500

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

6xy-9y²+18y

Multiplying binomials

100

(x + 6) (x + 3)

x² +9x +18

200

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

6x² + 7x - 20

300

(x - 8)(2x + 3)

2x² - 13x - 24

400

(y + 9) (y + 9)

y² + 18y + 81

500

(x - 12)(x + 12)

x² - 144

Standard Form

100

Write in standard form.  What is leading coefficient and degree? -2x^3+3x^2-4x+5 

Leading coefficient: -2

Degree: 3

200

Write in standard form.  What is the leading coefficient and degree?

y³ + 5y- 6 - 7y⁸

-7y⁸ + y³ + 5 y -6

Leading coefficient:  -7

Degree: 8

300

Write in standard form.  What type of polynomial, what is leading coefficient and degree?

10m² - 1/2 m⁹

-1/2m⁹ + 10m²

^binomial

^{LC:  -1/2}

^{D: 9}

400

Write in standard form. 

What is LC, degree and type of polynomial?

b⁵ - 3b - .7b¹⁰

-.7b¹⁰ + b⁵ -3b

L:  -.7

D: 10

trinomial

500

Write in standard form.  What is LC, type of polynomial and degree?

-.075x⁷

LC: -.075

D: 7

monomial

It is in standard form. 

Solve

100

The solutions to 

(x-4)(x+2) = 0

x = 4, -2

200

The solutions to 

1/2p(p - 5)(2p - 6) = 0

p = 0, 5, 3

300

Solve. 

5x² - 10x = 0

x = 0, 2

400

Solve. 

m²  + 6m + 9 = 0

m = -3 repeated root

500

Solve. 

3x³ + 3x² -6x = 0

x = -2, 1