Polynomials

Definitions

100

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

a term

200

DAILY DOUBLE

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

Factorise the polynomials

100

x² - 9

(x+3)(x-3)

200

What is the GCF of the following:

- 3x² - 3x - 60

-3 or 3

300

Factor completely. 

4x²  - 2x + 24

(4x - 6)(x + 4)

400

Find the length and width of a square with an area of 

9x²+48x+64

(3x+8)(3x+8)

500

Factor completely. 

32x²+24x-80

8(x + 2)(4x - 5)

Even more Random Polynomials

100

The degree of this polynomial: 

x³ - 7x² + 4x⁵ - 19x⁷

7

200

Classify by its degree and number of terms:

10x

Linear Monomial

300

A constant polynomial has a degree of this.

0

400

Rewrite this polynomial in standard form 

-6a⁴ + 10a³ + 14a⁷ - 22a² + 33

14a⁷ - 6a⁴ + 10a³ -22a² +33

500

Refers to the highest exponent in a polynomial, or the exponent on a specific term

Degree

Applications

100

Find the area of a room that is (3x - 5) ft by (2x + 1) ft.

6x² - 7x - 5 ft²

200

DAILY DOUBLE

What are the dimensions of a rectangular prism with a volume of 15x³+ 52x²+ 32x?

(x)(5x + 4)(3x + 8)

300

What are the dimensions of a rectangular prism with a volume of 18x³+ 84x²+ 48x?

(6d)(3d + 2)(d + 4)

400

A storage bin in the shape of a rectangular prism has a volume of 10x³+ 9x²+ 2x. What linear expressions can represent possible dimensions of the bin?

x,  5x + 2,  2x + 1

500

What are the dimensions of a rectangular prism with a volume of 32x³+ 224x²+ 360x?

(8x)(2x - 5)(2x - 9)

Trivia

100

This type of product excludes the middle term

Difference of squares

200

This product includes a middle term and has perfect squares for the first and last term.

Perfect Square Trinomial

300

Factorising a trinomial leads two a product of two of these 

Binomials

400

When looking at the area model, one observation about the across from each other includes that the ______________ are equal.

cross products

500

When using algebra tiles to factor a polynomial the goal is to create this

Rectangle, find the length and width.