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Colorful Diagrams
Rolle's Theorem
In street talk, Rolle's theorem says "if we have a chunk of a continuous function that begins and ends at the same yvalue  somewhere on that chunk, there's a horizontal tangent". Since the slope of the tangent is f '(x), and a horizontal line has slope = 0, there's a point on the chunk where the derivative is equal to 0.
Color Coded Explanations
The acronym is BEMDAS or BEDMAS
for brackets, exponents, multipication, division, addition, subtraction.
(with Multiplication & Division, Adding & Subtracting  order doesn't matter.)
example
Simplify 5 [ 2x + 3(x^{2}  7x + 6) ] + 3 [2x  4 (x^{2}  8x + 1)  7 ]
1st: multiply the inner parentheses ( ) by their coefficients + 3 and  4.
2nd: collect like terms within the brackets [ ].
3rd: multiply the brackets [ ] by 5 and by 3, and collect like terms.
1st: 5 [2x + 3x^{2}  21x + 18] + 3 [2x  4x^{2} + 32x  4  7] =
2nd: 5 [3x^{2}  19x + 18] + 3[ 4x^{2} + 30x 11] =
3rd: 15x^{2}  95x + 90  12x^{2} + 90x  33 =
3x^{2}  5x + 57
"Side by side" math and explanations
if you don't understand how to get from one step to the next, the explanation is right there beside the math  you don't have to read through a whole paragraph to find what you need.
2 [3 (x + 1)^{ 2} + 4( x^{ 2}  3)] + 6x  5 =  square (x + 1), multiply 4(x^{2}  3) 
2[3(x^{ 2} +2x +1) +4x^{ 2} 12] + 6x 5 =  multiply 3(x^{ 2} + 2x + 1) 
2[7x^{ 2} + 6x  9] + 6x 5 =  collect like terms in brackets [ ] 
14x^{ 2}  12x + 18 + 6x 5 =  multiply 2[ 7x^{ 2} + 6x  9] 
14x^{ 2}  6x + 13  collect like terms 
Clear, Easy to Understand Explantations
Why in the world is a minus times a minus equal to a plus???
Say you owe me $10.00 but you have no money in your pocket now to pay your debt.
You have $10.00 (negative ten dollars); you owe me $10.00 and you have nothing  right?
I'm feeling generous for some strange reason and I say "Forget about the $10 you owe me."
Now, you have $0 , which is $10 more than you had before I took away a debt of $10.
The 1st minus sign instructs us to take away (an operator) and
the 2nd minus sign is the negative quality of the $10.00, because it is a debt.
So  ( 10) = + 10 and 5x  ( 3x) = 5x + 3x = 8x.
and 3a  2( 5a ) = 3a + 10a = 13a
So, just as a minus sign can mean 2 things:
the operation to subtract, or
the negative quality of loss or debt or retreat (down or left)
a plus sign can also mean 2 things:
the operation to add, or
the positive quality of a gain or advance (up or right).
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