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29 Cards in this Set
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exponents: multiplying powers with the same base
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(x^m)(x^n)=x^(m+n)
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exponents: dividing powers with the same base
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(x^m)/(x^n)=x^(m-n)
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exponents: raising a power to an exponent
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(x^m)^n= x^mn
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exponents: multiplying powers with the same exponent
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(x^n)(y^n)=(xy)^n
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exponents: dividing powers with the same exponent
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(x^n)/(y^n)=(x/y)^n
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combining like terms
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2a+3a=(2+3)a=5a
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adding or subtracting polynomials
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combine like terms
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multiplying monomials
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multiply coefficients separately
2x*3x=(2*3)(x*x)=6x^2 |
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multiplying binomials
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multiply using FOIL
First terms Outer terms Inner terms Last terms then add and combine like terms |
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multiplying polynomials
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multiply each term in the first polynomial by each term in the next polynomial
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dividing polynomials
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use long division just like with numbers
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common forms of factoring
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factor common to all terms
difference of squares squares of binomials |
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factor common to all terms
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ax+ay=a(x+y)
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difference of squares
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a^2-b^2=(a-b)(a+b)
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square of binomials
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a^2+2ab+b^2=(a+b)^2
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for unconventional factoring problems
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pick a couple numbers and plug them in the question and answers to see which ones come out the same
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Golden Rule of Equations
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Whatever you do to get the target variable or expression by itself, do the same thing to both sides.
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solving for an unknown in a denominator
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multiply by the denominator or cross multiply to remove the fractions
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solving for an unknown in an exponent
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re-express one or both sides so that the two sides have the same base, then you can pull out the exponent expressions and have them equal each other
8^x=16^(x-1) (2^3)^3=(2^4)^(x-1) 2^(3x)=2^(4x-4) 3x=4x-4 3x-4x=-4 -x=-4 x=4 |
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Quadratic Equations
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1. Write in this form: ax^2+bx+c=0
2. factor the left side 3. seat each factor to equal 0 4. solve each |
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If the left side of a quadratic equation is not factorable, you can use the quadratic formula:
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x=(-b [+or-] sqrt[b^2-4ac])/2a
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"In terms of" equation solving
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multiple variables, solve for the variable in terms of the others
3x-10y=-5x+6y Solve for x in terms of y. -isolate x. |
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simultaneous equations
4x+3y=8 and x+y=3, solve for x and y |
combine the equations so that one variable cancels out.
(x+y)(-3)=3(-3) -3x-3y=-9 4x+3y=8 x=-1 -1+y=3 y=4 |
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absolute value
|x-12|=3 |
split the equation into two equations, then solve
x-12=3 or x-12=-3 x= 15 or 9 |
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absolute value and inequality
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isolate the variable. If you multiply or divide both sides by a negative, the </> sign must be switched to its opposite.
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If n>0
|whatever|<n |
-n<whatever<n
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If n>0
|whatever|>n |
whatever<-n OR whatever>n
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|2x-3|<7
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-7<2x-3<7
-4<2x<10 -2<x<5 |
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|(3x+9)/2|>7
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(3x+9)/2<-7 OR (3x+9)/2>7
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