Review for Algebra Test over Polynomials…

Use laws of exponents, Distributive Property, CLT,

addition, subtraction, multiplication, and division of

polynomials. Also, find and use GCF.

The 2nd power mean…

WRITE THE PARENTHESIS TWICE!

( 3p + 4 ) ( 3p + 4 )

9p2 + 12p + 12p + 16

CLT

+ 24p9p2 + 16

“subtracted from” means…

(2q + 6 ) goes first!

(2q + 6 ) – ( 7q – 3 )

2q + 6 – 7q + 3Distribute the minus sign.

C.L.T.

– 5q + 9

To find the degree…

ADD all the powers in the term.

3 + 5 + 1 = 9

Ninth degree

We are given the perimeter:

12x + 1

To find the missing side, first, look at the x-terms .

4x + 5x + ( ? ) = 12x

3x

Now look at the numbers:

+5 + (– 8) + ( ? ) = 1

positive 4

3x + 4

Area of a triangle:

2

bhA

3 2(5 ) 4

2

w wA

Do the Power to a Power FIRST!

(multiply the powers…)2 3 25 w 625w

625 4

2

w wA

Multiply & Divide numbers:

25 • 4 ÷ 2 = 50

50w7

When you multiply w6 times w…

add the powers!

Perimeter means…

ADD ALL SIDES!

Label them.3m + 4

2m – 5

C.L.T.

Add all the m-terms…

2m + 3m + 2m + 3m =

10m

Combine the numbers:

+4 + 4 – 5 – 5 = – 2

– 2

Binomial (2 terms) times a Trinomial (3 terms) means…

6 multiplications

b • b2 = b3

b • 2b = 2b2

b • (–5) = –5b

b3 + 2b2 – 5b

3 • b2 = 3b2

3 • 2b = 6b

3 • (–5) = –15

+ 3b2 + 6b – 15 CLTHighest power first!

b3 + 5b2 + 1b – 15

Add the powers!Add the powers!

= x12

Multiply the powers!Multiply the powers!

= x12

Subtract the powers!Subtract the powers!

= x12

The zero power means…The zero power means…11

The negative power means…The negative power means…the reciprocal.the reciprocal.

(the x(the x1212 moves to the moves to the numerator)numerator)

= x12

Area of square:

A = length • widthc + 6

( c + 6 ) ( c + 6 )

c2 + 6c + 6c + 36CLT

+ 12cc2 + 36

2x2 – 2xy + 3xy – 3y2

CLT+ xy2x2 – 3y2

4n2 – 6n + 6n – 9CLT

4n2 – 9

Volume of a rectangular prism:

V = Bh (B is the area of the base)The “base” is a rectangle… length • width

V = l•w•h(2xy4)(3x2y)( x + y )Multiply the first

2 monomials…

Multiply #’s and ADD the Powers!

6x3y5 ( x + y )Distributive

Property

6x4y5 + 6x3y6

Sum means ADD.

CLT1y2 + 1y2

2y2

Product means MULTIPLY!

n2 + 5n + 4n + 20CLT

+ 9nn2 + 20

Perimeter means ADD ALL

SIDES!

Label them.

p2 – 2p + 3

6p + 1

Do not use the 5p. Do not use the 5p. That’s the height.That’s the height.

CLTStart with the highest power.

p2 + p2

2p2

(-2p) + (-2p) + 6p + 6p

+ 8p

+3 + 3 + 1 + 1

+ 8

The GCF consists of:

The biggest number that will divide into 8 and 12…

4

and the common/shared variables… c and d

Take the lowest power.

c2 and

c d2 3

d3

a. NOT Like Terms… Cannot be simplified!

b. Multiply #’s and… Add the powers.

= 24x7

c. Power to a power… Multiply the powers.

(x0)7 = x0

Anything to the 0 power equals 1.24 • 1 =

= 24d. NOT Like Terms… Cannot be simplified!

GCF consists of:

The biggest number that will go into 20 and 30…

10

AND, the common variable(s) with the LOWEST POWER…

y6

10y6 ( )

Divide both terms by 10y6 and put the results

in the parentheses.

10y6 10y6

2 + 3

y (8 – 6)

y2

Quadratic 2nd power Trinomial 3 terms

TRUE

Cubic 3rd power Binomial 2 terms

FALSE

5th degree 5th power Monomial 1 term

TRUE

linear 1st power Binomial 2 terms

TRUE

Distributive Property

Multiply the #’s and add the powers!

15x4 + 6x2

Multiply #’s and Add the powers: 6m –

2

n0 equals 1…GOES AWAY!

m–2 means…the reciprocal.

(It goes in the bottom)

26m

Distributive Property

Distribute the minus sign.

– 7d2 – d + 5d2 – 4d + 3 CLTCLT

– 6d2 – 5d + 8

a2 – 5a + 5a – 25 TRUE

ADD…CLT a + a + 5

2a + 5

FALSE

( a + 5 ) ( a + 5 )a2 + 5a + 5a + 25

a2 + 10a + 25

FALSE

12x2 + 18x – 10x – 15 CLT + 8x12x2 – 15

Area of a rectangle:

A = bh

We know A and b.

To solve for h…

divide!3 236 12

12

x x

x

3x2 + x

36 ÷ 12

x(3 – 1)

12 ÷ 12

x(2 – 1)

A

b

20 ÷ 4

g(10 – 3)

5g7

– 4 ÷ 4

g(7 – 3)

– 1g4

28 ÷ 4

g(3– 3) = g0 = 1

+ 75g7 – g4 + 7

The power outside the

parentheses applies to

everything in parentheses.

43 = ?

64

Power-to-a-Power:Multiply powers!

a6•3 = ?

a18

b5•3 = ?

b15

6k3 + 4k – 10 – 5k2 – 6k + 9CLT

6k3 – 5k2 – 2k – 1

STUDY!STUDY!