Post on 31-Dec-2015
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!