Advanced Algebra

A line contains the points (5, -4) and (4, -6). What is the slope of the line perpendicular to it?

(-1/2)

The slope of the line is 6. The slope of the line perpendicular to the aforementioned line is

(-1/6)

The slope parallel to that of the line 6x-4y=12

(3/2)

Factor 3x^2 - 4x - 4 completely

(3x+2)(x-2)

Power of a power rule

(X^A)^B=X^(AxB)

Product of Powers Rule

(X^a)x(X^b)=X^(a+b)

Formula for finding slope

(Y2-Y1)/(X2-X1)

Coefficient (https://www.mathsisfun.com/definitions/coefficient.html)

A numerical constant quantity placed before (and multiplying) the variable in an algebraic expression or equation (4 IN 4xy^2)

Variable (http://mathinsight.org/definition/variable) (https://www.mathsisfun.com/definitions/variable.html)

A quantity that may change within the context of a mathematical equation or experiment; a symbol for a number that we do not yet know the value of.

Point-slope form

For this one, they give you a point (x1, y1) and a slope m, and have you plug it into this formula: y - y1 = m(x - x1)

Zero product property

If the product of two quantities is zero, then a least one of the quantities must be zero.

Integers

Natural numbers (positive integers), zero, and negative integers. Negative integer is the opposite, or additive inverse, of a positive number.

Whole numbers

Natural numbers and zero (0, 1, 2, 3, 4)

Linear: --(A/B)

Slope (Negates the numerator and the denominator)

Y=Mx+B

Slope-intercept equation of a line

Natural numbers

The numbers used for counting: 1, 2, 3, 4

Absolute value (http://www.purplemath.com/modules/absolute.htm)

distance of a number from zero, without regard to its sign

Additive inverse (https://en.wikipedia.org/wiki/Additive_inverse)

opposite of a number that, when added to a given number, yields zero

Simplify p(p-2q) + 3(pq - q^2)

p^2+pq-3q^2

If a quadratic (Ax^2 +/- By +/- C) is difficult to factor, you can use the...

quadratic formula

The slope of a line parallel to another line is

the same

Which equation is equivalent to 15x+3y=10?

y=-5x+(10/3)

Find the prime factorization of 1350

2x3^3x5^2

Factor 3x^3-27x completely

3x(x+3)(x-3)

Express (3t-4)(2t+3) as a simplified polynomial

6t^2+t-12

Algebraic expression (http://home.avvanta.com/~math/def2.cgi?t=expression)

A mathematical phrase that can contain ordinary numbers, variables (like x and y), and operations (add, subtract, multiply, or divide).

Multiplicative inverse (https://en.wikipedia.org/wiki/Multiplicative_inverse)

A number X, denoted by 1/X or X^-1 (which are the same thing), is a number which, when multiplied by X, is equal to one. (1/X)x(X/1)=(X/X)=1

Solution of an equation (https://www.google.com/search?q=solution+of+an+equation+definition&oq=solution+of+an+equation&gs_l=serp.1.1.0i71l8.0.0.0.4283.0.0.0.0.0.0.0.0..0.0....0...1c..64.serp..0.0.0.PmE0TvR1ROY)

A value or values which, when substituted for a variable in an equation, make the equation true

Square of a difference rule

A-B)^2=A^2-2ab+B^2

Difference of two squares rule

A^2-B^2=(A-B)(A+B)

QUADRATICS

B^2-4(A)(C) >0 two solutions =0 one solution <0 no real solutions, 2 imaginary solutions

Slope of a vertical line

Undefined

Linear: (C/A, 0)

X-Intercept

Express ax(x-a)(x+a) as a simplified polynomial

ax^3-a^3x

Factor 4t^2 + 4t + 1 completely

(2t+1)^2

What is the y-intercept of a line whose equation is y+9=2(x-3)?

Negative 15

Ax+By=C

Standard form

Sample space (http://www.regentsprep.org/regents/math/algebra/apr4/Lsample.htm)

The set of all possible outcomes for an activity or experiment (Roll a die: 1, 2, 3, 4, 5, 6). (Flip a coin: 1, 2).

Opposite (http://www.mathgoodies.com/glossary/term.asp?term=opposites)

Two integers are opposite of they are the same distance away from zero, but one is negative and one is positive

For the equation of the line 4x-5y=-20 find The x-intercept The y-intercept The slope

X-Intercept (-5,0) Y-intercept (0,4) Slope (4/5)

Simplify (-X^3)^2(X^4)

X^10

Simplify (X^3 - 3x^2 - 2x + 5) - (X^2 - 2x + 2)

X^3 - 4x^2 + 3

Quotient of powers rule

X^a/X^b=X^(a-b)

Linear: (0, C/B)

Y-Intercept

Slope of a horizontal line

Zero

Solve the equation 6x^2=5x-1

[(1/2), (1/3)]

Square of a sum rule

(A+B)^2 = a^2+2AB+B^2

Conjugate Binomials

(A-3) (A+3) =A^2 - 9 (A+B) and (A-B)

Reciprocal (https://www.google.com/search?q=reciprocal&oq=reciprocal&aqs=chrome..69i57j0l5.4023j0j7&sourceid=chrome&ie=UTF-8)

(of a function) related to one another such that their product is 1 (X/1)x(1/X)=(X/X)=(1/1)=1

Algebraic Definition of Absolute Value

- If x is greater than or equal to zero, then the absolute value of x=x -If x is less than zero, then the absolute value of x=-x

Properties of Inequality

Chart #4

Proof of the quadratic formula

Chart #5

This is the process used to multiply two binomials

F.O.I.L.

Rational numbers

All the numbers can be written as quotients as integers. Must have a nonzero denominator. Some rational numbers can be written as terminating numbers. All other numbers can be written as repeating decimals

Irrational numbers

Cannot be written as quotients of integers Decimal representations neither terminate nor repeat If a positive number is not a perfect square, its square root is irrational

Properties of Natural Numbers

Chart #1

Properties for Simplifying Algebraic Expressions

Chart #2

Properties of Equality

Chart #3

Evaluate (algebra) (https://www.google.com/search?q=evaluate&oq=evaluate&aqs=chrome..69i57j0l5.3599j0j7&sourceid=chrome&ie=UTF-8)

Find a numerical expression, solution, or equivalent for

Term (https://simple.wikipedia.org/wiki/Term_(mathematics))

Either a number or variable, or the product of several numbers or variables, separated by a sign, + or - in an overall expression or equation

If you want to determine whether or not a quadratic (Ax^2 +/- By +/- C) is factorable...

determine whether or not descriminant of a quadratic equation is a perfect square (B^2 -4(A)(C)). If so, factorable; if not, not factorable.

the slope of a line perpendicular to another line is

negative reciprocal of the first slope