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INEQUALITY: X > 3
NUMBER LINE: <------O------->
INTERVAL: (3, ∞) |
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Definition
Intervals = (1,5] always follow the number line
<, > = always use open round parenthesis ( )
≤, ≥ = always use brackets [ ]
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Definition
Change positions
5+6 = 6+5 |
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Definition
You can move parenthesis ( )
a(bc) = (ab)c |
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Definition
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Definition
it is the opposite of a
a is 4, then -a would be -4
a=-2 then -a=2 |
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Fractions
Multiplying
Dividing
Adding and subtracting |
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Definition
*Always multiply accross
1/3 . 2/5=2/15
*keep it, change it, flip it
1/3 divide by 2/5 = 1/3 . 5/2= 5/6
*fin common denominator
1/3 + 2/5= 5/15 + 6/15= 11/15 |
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Definition
anything to the zero power is ONE
and just modify inside ( )
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Definition
| you will need to change it to a positive by crossing it over the magic division bar |
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| adding or multiplying exponents |
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Definition
(x^2)-^2 multiply exponents
x-^4
x^2 . x-^2 add the exponents
x |
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Term
| Radical and Exponential form |
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Definition
| when you have a 3 radical then to write the exponential form grab the outside and put it on bottom and the power inside putt it on top and you will get 3^1/2 |
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How do you get from 10 - radical 50/15 to its simplify answer 2 - radical 2/3
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Definition
start with radical 50 = radical 2.5.5 =5 radical 2
replace 10 - 5 radical 2/15 then if we divide all three number by 5 the end result is
2- radical 2/3
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Definition
fin domain
Is it a polynomial?
x^2+x+2 = all real numbers
What if it has a denominator with an x
x+2/x-1 the bottom = 0 or x-1 =/ 0
If it has a radical
x-3 radical stuff under it >/ 0
x-3 >/ 0= x >/3 |
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Definition
R= 45X
COST= 100 + 10X
Find the profit of making 10 chairs
(45x)-(100+10x)
(45x)(-100-10x)= 45x-100-10x
45x-10x= 35x-100 (Px)
35(10)-100
=$250 profit |
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Multiplying Polynomials
*each term of the first polynomial must be multiplied by each term*
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Definition
(5x+3)(-6x^2+15x-4)
5x by term= -30x^3+75x^2+ -20x
3 by term= -18x^2+45x+ -12
= -30x^3+55x^2+25x-12
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FOIL
*each term of first polynomial times each term of second polynomial* |
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Definition
(2x-4)(x+5)
=2x^2+10x-4x+20
=2x^2+6x+20 |
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Definition
(5x+9)(5x-9)= 25x^2-45x+45x-81
= 25x^2-81
this is no the same as
(5x+9)^2= (5x+9)(5x+9)= 25x^2+45x+45x+81
= 25x^2+90x+81 |
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Factoring Polynomials
"factor out common factors" |
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Definition
15x+9= 3(5x+3)
7x^3-10x^2+x= x(7x^2-10x+1)
6x^3-4x= 2x(3x^2-2)
(x-2)(2x) + (x-2)(3)
=(x-2)(2x+3) |
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Definition
Difference of square: u^2-v^2=(u+v)(u-v)
Perfect Square Trinomial: u^2+2uv+v^2 and
u^2-2uv+v^2
Perfect trinomial: x^2-10x+25= (x-5)(x-5)
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Definition
If you recognize another square then factor it, always look for more.
you cannot factor if you see a sum of square (4x^2+9)
If you want to verify your answer then the terms has to be the middle term of the original problem. |
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Definition
x^3-2x^2-3x+6=(x^3-2x^2)-(3x+6)
change - to + and change signs
(x^3-2x^2) + (-3x-6)
x^2(x-2) + -3(x-2)
= (x-2)(x^2-3) |
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| COMPLETELY FACTOR EXPRESSION |
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Definition
x^4-6x^2+x^2-6x = (x^4-6x^2)+(x^2-6x)
x^3(x-6) + x(x-6)
=(x-6)(x^3+x)
final answer=(x-6) (x)(x^2+1)
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Definition
factor out 3x
21x^3-9x^2+3x
=(3x)(21x^3/3x - 9x^2/3x + 3x/3x)
=(3x)(7x^2 - 3x + 1) |
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