MATH HOWTO

Factoring

To express a polynomial as the product of monomials and polynomials in other words, the reverse of factoring, this is finding the common greatest factor, you divide the platform or the coefficient and then subtract the factors off the variable the variable x or y has to be common on the three polynomial for it to be consider, if no letters are common then the greatest common factor number gets used without letters

5(3x)^2

the factors from this equation are are followed 5. 2x. 2x. 2x

factoring greatest common factor 2

the greatest of the common factors of two or more numbers Factoring is the opposite of distributing. When distributing, you multiply a series of terms by a common factor. When factoring, you seek to find what a series of terms have in common and then take it away, dividing the common factor out

Lease Common Multiple

the least of the common multiples of two or more numbers

(5x)^2

the trick with this problem is that should X equals to 2, you have 5.2 square 2 10.10 = 100 --- Now , if there is no referencing of the X then you can consider it a one 5x .5x = 25x

factoring by grouping 2

the use of the distributive property to factor polynomials having four or more terms make note that the sign in front of the block is what matters, if negative, the equation is that, or possitive.

Exponent expressions

these are powers of 2 or cube if the problem has an even number of negatives, the result is positive. if the number of negatives are odds, the answer is negative. -4^2 = -16 (-4)^2 = 16

finding the number of a percent

this example we have 20 and out of that we have 25%. 25/100 x 20/1 = 500/100 - 5/1 = 5 you always put number over 1

Make note that any negatives in front of a number should be consider

this means that if a negative number is in front, that becomes a negative, never think its subtraction, its a nevative interger

ZERO in math

times tables zero means 0 division 0 means 0, so 4 / 0 = 0 dont forget to add the zero if you drop the zero and divisor devices with it, the answer is 0

Fractions ( adding and subtracting )

to add, find a common denominator then multiple both num and denominator, and then add the numbers that made the denominator 1/3 + 1/2 = 5/6 6 is the least common denominator 3 x2= 6 2x3=6 so 1x3 =3 and 1x2 =2 = 5 subtraction is the same 3/5 - 1/3 = 4/15 5x3=15 so 3x3 = 9 3x5=15 so 1x5 = 5 9 - 5 = 4 total 4/15

relocate negative exponents

to the bottom or top

plus negative

what is means is that you make the minus into a plus, and you add a negative to the positive then subtracted, this works mostly for subtracting intergers minuted 10 - 3 subtrahed = 7 difference adden 10 + addend 3 = sub total 11 if subtracting a positive to a negative

multiply decimals

what you do is remove the decimal, but then add it back as many times each side had 3.64 x 2.4 = 8.760 = x3 dots to move or decimals,

rational number

A number that can be written as a fraction if we can write it as a fraction its a rational -5 = -5/1 or -45/9 rational can be written as a fraction. 0.25 if you fraction it you can consider it a rational number.

even and odd numbers

Even numbers end in 0, 2, 4, 6, or 8; number divisible by 2 Odd numbers end in 1, 3, 5, 7, 9 - anything else that is left over

4 polynomial factoring

if you have to remove all the X factors off, you can put a 1 as what should remind.

Subtract the polynomials (4x^2 + 5) - (-2x^2 +4x - 7)

1. distribute a -1 into the second polynomial 2. remove the parentheses 3. combine like terms

percent to fractions

1. remove % 2. write the number from step 1 in the numerator and write 100 as the denominator 3. simplify This not like making a decimal into a fraction, so dont add 10000 but only 100

Divide Polynomials (Binomial Divisor)

3 / 3 = 1 and rewrite the negative exponent.

multiply fractions

3/5 x 10/8 = 30/40

expression

A mathematical phrase that contains operations, numbers, and/or variables. x=3 4x^2 = 4.3.3 - 12.3 = 36 remember multiply let to right

scientific notation

A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10. here you see positive moves right and negative to the left side the decimal cannot be in two digits but one.

prime factorization

Breaking down a composite number until all of the factors are prime

factoring po main

Difference in squares reverse foil or AC method - and + factor by grouping

Subtracting polynomials

Distribute the negative ( keep change flip ) then combine like terms on the second polynomial put a -1 and do distributed multiplication, and then ADD the like terms like you do for adding polynomial

evaluate

Examine and judge carefully.

monomial times polynomial

First multiply the coefficients. Then "multiply" the variables by ADDING together the variable's exponents. Remember a variable with no exponent has an implied exponent of 1. ( [2y2][y3 + 2 xy2z = 4z] = 2y5 + 4xy4z + 8y2z)

Polynomial

If divided by + or - and has 2 or more, it can be called polynomial. trinomal are three terms or more but people often call it polynomial 3x + 7 - poly 5x - monomial 3x - 4 + 4 = trinomial

SUBTRACTION

In subtractions the large number goes on top and smaller below. 8 - 3 = 5 8 - minued 3 - subtrahend 5 - difference he smaller number which is subtracted is called subtrahend. 4629 → Minuend -1213 → Subtrahend 3416 → Difference The resulting number is called the difference.

factorization when starting with a variable

In this example we start with X, so what you do is distribute the X and find a common greatest factor of 10 that subtracts or adds to 3

divide fractions

Keep Change Change 3/4 / 2/7 3/4 x 7/2 21/8 simplified 2.5/8

irrational numbers

Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating. numbers that cannot be equally fraction a number that finish the division with a quoten

subtracting intergers

Plus negative convert the minus to plus, and make negatives to positive add opposites, meaning 9 - (-2) = 11 takes the sign of the highest number 9 + 2 = 11 same sign you subtract, starting at the left to right, -11 - (-5) = rewrites -11 + 5 = -6 -11 + 5 = -6 do a number line to get a feel where to go, you head to wards the positive sign

binomial multiply binomial

Remember foil: first, outer, inner, last. Combine like terms by adding/subtracting.

Subtracting negatives

Subtracting a positive number from a positive number - it's just normal subtraction. 6 - (-3) = 3 Subtracting a positive number from a negative number - start at the negative number and count backwards. (-2) - 3 = -5 Subtracting a negative number from a positive number - turn the subtraction sign followed by a negative sign into a plus sign. So the equation turns into a simple addition problem 2 - (-3) = 5. Subtracting a negative number from a negative number - a minus sign followed by a negative sign, turns the two signs into a plus sign. (-2) - (-4) = 2. note: maybe if the larger negative is -4 and you subtract -3 you could end in -2

zero product rule

The Zero Product Rule states: If A and B are any two quantities such that (A)(B) = 0, then one of the following must be true: A = 0 or B = 0

Convert a fraction to a decimal

The numerator goes inside the bracket, and the denominator outside, then you devide. always adding a period as you cancel numbers out 2/3 = 0.66 a slash on top of the 6 means infinite

Factoring a polynomial

The process of rewriting a polynomial as a product of polynomial factors. Factoring in short terms means cancel out numbers out to make the polynomial easier to fraction GCF : greatest common factor it means finding a common number we can factor out numbers. foil and distributed subtract the exponents, divide the common greatest factor on each side.

Math word problems

The third step is to look for "key" words. Certain words indicate certain mathematica operations. Below is a partial list. Addition: increased by more than or then combined, together total of sum, plus added to comparatives ("greater than", etc) Subtraction: decreased by minus, less difference between/of less than, fewer than left, left over, after save (old-fashioned term) comparatives ("smaller than", etc) Multiplication: of times, multiplied by product of increased/decreased by a factor of (this last type can involve both addition or subtraction and multiplication!) twice, triple, etc each ("they got three each", etc) Division: per, a out of ratio of, quotient of percent (divide by 100) equal pieces, split average Equals is, are, was, were, will be gives, yields sold for, cost

Factoring A-C method

This method is when we multiply A and C . 12^2 + 5x - 2 1. start by multiplying A and C 2. find a sum that equals to B by adding or subtracting - in blue shows - you'd have to do both positive and negative, but as longest the ADDING equals to 5 positive 3. break the middle/B into the sum that we got earlier 3 and 8, each being identical as the 5x; 3x and 8x, each becoming a four polynomial 4. then you the greatest common factor to divide each side to get a sum.- factoring in mathematical terms 5. then we combine the like terms, factoring again,

Trinomial Factoring using reverse foil

To successfully factor a trinomial, one must reduce the equation so that the highest power must be 1 and each monomial must be separated by multiplication; an example of a factored trinomial is (x + 4) (x - 5) from (x2 - x - 20). on the example the last number which is C was used to make the math formula divide the C then add add to get the results

inverse operations equation

Two operations that undo each other

Simplify a rational expression

Write the fraction so there are no common factors other than 1 or -1 the condition means that as longest x doesn't equals the number in front or ZER0

coeficient

a number that is multiplied by a variable

prime number

a whole number that can be divisible by itself and one. 3/1 = 3 or 3/3 = 1 the number has to divide evenly with another number 2, 3, 5, 7, 11 are prime, so what makes a non-prime number is a number that can be divided by other numbers besides one and itself.

adding intergers

add numbers with the same signs subtract numbers with different signs

Scientifi Notation 1

add the exponents, so if negative you subtract.

Exponents - Multiplying numbers with same base

add their exponents (6^2 *2^3 = 6^5)

Adding intergers

if the signs are the same, we add, but if the signs are different we subtract and keep the value of the number that is greater. -3 - 5 = -8 -3 + 5 = 2 - we subtract ++ = + - - = + when

Adding polynomials

combine like terms adding is mostly how you resolve it. subtraction and adding like terms,

inverse of multiplication

division

is

equal

Adding Fractions and fraction

find a common denominator then add/subtract the numerator, div/multiplication doesn't matter you multiply across add the numerator leaving the denominator the same

factors divide evenly

if a number does not divide evenly is not a factor.

Exponents mistakes

if the exponent follows, -2^2 = -4 but (-2)^2 = 4 inside the parenthesis is positive, outside is consider negative or whatever the number is.

Consecutive integers

integers in counting order 2 4 6

exponents come after the parenthesis

keep note after the paren you do the exponents

factoring by grouping steps

make sure the two sides parenthesis match

EXPONENTS- Addition & Subtraction

multiplication you add division you subtract

Multiply Polynomials

multiply each term in one polynomial by each term in the other polynomial add those answers together, and simplify if needed

variables are always 1

never forget that x, or y its usually a one 1, so don't ignore that or else you'd get the wrong answer.

descending oder polynomial

numbers by their own are lowest

Dividing Integers

positive/positive and negative/negative= positive; positive/negative= negative

polynomials distributed multiplication

regular distirbuted multiplication then add like terms keep in mind that variables infront add to the distributed process x(x = x^2

Diving Decimals

remember 2.3 / 44 rewrites 23/440 then you add the decimal point at the end. decimals goes at the end of whole numbers.

monomial times monomial

remember a variable with no exponent has an implied exponent of 1. First multiply the coefficients. Then "multiply" the variables by ADDING together the variable's exponents. ( [3 x4 y2 z][2 y4 z5]= 6 x4 y6 z6)

factors

rewriting an expression as the product of its factors

Graphis line

slope is = M yint = B do slopes first which is the M then do the Y

factor

something that contributes to a result

x . x

square x2

product

the answer to a multiplication problem

Fractions - Division

when the divisor is a decimal 1.4 you move the dividend the same amount of digits the divisor has

foil or distributed multiplication

works only with to polynomial First outer inner last

Negative Exponent Rule

x ⁻ⁿ = 1/xⁿ

Negative Exponent Rule

x ⁻ⁿ = 1/xⁿ https://www.youtube.com/watch?v=g5ZGDNxJwxA 1. quotient rule of exponents 2. relocate values, then simplify re-write the negatives to the opposite location using positive exponents if the lower denominators are common bases, you use product rules of adding the X to total a bigger number; opposite than subtracting. The re-write rule applies to only exponents or variables.

Reverse Foil

x^2+(b+a)x+ab=(x+a)(x+b)

Exponent Multiplication

you add them, divide you subtract, sum/subtract only do if base are the same.

addition decimal and subtraction

you aligned the decimal points and then do the task

Division or Multiplication fractions

you can pre-simplified to make an equation smaller also you have to remember with division is keep change and flip

primefactorization

you put how many times a number exist in a group, so if 2 is 3 times the most, that is what you use. if 4 is 1 time the most, that is your answer.

Quadratic Formula

you start by factoring the equation