Polynomials!!!

Definitions/Rules of Polynomials

100

Ordering a polynomial from largest exponent to smallest is known as .......

Standard Form

ex: 2x²+9x-4x⁴+17 

Becomes: -4x⁴+2x²+9x+17

200

When adding polynomials we __________

 and NEVER _________

Combine Like Terms

Change Exponent

ex: (5t²+6t)+(3t²-7t)

Becomes: 8t²-1t

300

What is the first step you need to complete when subtracting polynomials?

You must complete Keep - Change - Change

ex: (4x-9)-(2x+6)

Becomes: (4x-9)+(-2x-6)

400

When multiplying binomials we must __________ each term in the first binomial by each term in the second binomial. 

Multiply/distribute

ex: (r+2)(r-5)

Becomes: r(r)+r(-5)+2(r)+2(-5)

r²-5r+2r-10

r²-3r-10

500

When factoring by GCF Method we first find the __________ of the coefficients and then check the __________ of the terms and pull out the _________ exponent among the variables.

GCF

Variables

Smallest

600

When you multiply variables together we ___________ the exponent.

When we divide variables together we ___________ the exponents

Add

Subtract

ex: 

x²(x)=x⁽²⁺¹⁾=x³

x²/x=x^(2-1)=x

700

When factoring trinomials we split the middle term using the pair of factors that _____________________ and ___________________

Multiplies to the first(last) term

Adds to the middle term

Adding/Subtracting Polynomials

100

Simplify:

(-5y²+17y-3)+(9y²-7y+3)

4y²+10y

***Don't change the exponent***

200

Simplify:

(9ab³+3b³)+(4a³-5ab³+b³)

4a³+4ab³+4b³

***Can only combine terms with the EXACT same variables AND exponents****

300

Simplify:

(8f⁴-9f²)-(4f⁴+9f²)

4f⁴-18f²

***Keep-Change-Change***

400

Simplify:

(3g³+9g³h-2h³)-(7g³+3g³h-6h³)

-4g³+6g³h+4h³

***Keep-Change-Change***

500

The length of a rectangle is represented by L=(2x-4) ft.

The width of the same rectangle is represented by w=(5x+8) ft.

Using P=2(w)+2(L), find the expression that represents the Perimeter of the rectangle.

P=(14x+8) ft.

***Distribute the 2 to each term inside the parentheses***

Multiplying Polynomials

100

Simplify:

9y³(4y³)

36y⁶

**Add exponents of the same variable***

200

Simplify:

5s³t²(8st)

40s⁴t³

*** Variables without a visible exponent have an exponent of 1, we just don't write it*** 

300

Simplify:

8k⁴(k³-4k+12)

8k⁷-32k⁵+72k⁴

***Distribute 8k⁴ to ALL terms in parentheses***

400

Simplify:

(m+9)(m+2)

m²+11m+18

***Multiply both terms in the first binomial times both terms in the second binomial***

500

Simplify:

(5t-7)(t+5)

5t²+18t-35

***Bring the minus in front of the 7 with it when multiplying***

600

The length of a rectangle is represented by L=(2x-4) ft.

The width of the same rectangle is represented by w=(5x+8) ft.

Using A=Lw, find the expression that represents the Area of the rectangle.

A=(10x²-4x-32) ft²

***You can use the Box Method to help!***

Factoring Polynomials

100

Factor using the GCF Method:

6t³+9t²

3t²(2t+3)

***Find GCF of coefficients and smallest exponent of variable****

200

Factoring using GCF Method:

8w⁸-4w³+2w

2w(4w⁷-2w²+1)

***Must find GCF of ALL terms***

300

Factor using GCF Method:

-5r³+15r-20

-5(r³-3r+4)

***Pull negative out IF first term is negative***

400

Factor the Trinomial:

x²-9x+18

Hint: Don't forget negative times negative is a positive number!

(x-3)(x-6)

***Split middle and factor each half using GCF method***

500

Factor the Trinomial:

3x²+8x-3

(3x-1)(x+3)

***Look for the repeating bonimial when factoring!***