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)

Factor 4t^2 + 4t + 1 completely

(2t+1)^2

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

(3/2)

Factor 3x^2 - 4x - 4 completely

(3x+2)(x-2)

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)

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)

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

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)

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

Negative 15

Linear: --(A/B)

Slope (Negates the numerator and the denominator)

Y=Mx+B

Slope-intercept equation of a line

Ax+By=C

Standard form

Natural numbers

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

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).

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

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

the slope of a line perpendicular to another line is

negative reciprocal of the first slope

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)

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

QUADRATICS

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

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

Properties of Inequality

Chart #4

Proof of the quadratic formula

Chart #5

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

This is the process used to multiply two binomials

F.O.I.L.

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

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

Slope of a vertical line

Undefined

Linear: (C/A, 0)

X-Intercept

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)]

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

ax^3-a^3x

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.