Factoring+Polynomials

Vocab:
Factor- One of two or more expressions that can be divided evenly by another expression. Greatest common factor- The greatest factor that divides two numbers. Polynomial- An expression involving sum of powers in one or more variables multiplied by coefficients.

**Hand factor:**
Use when- - A is not equal to 1 Ex) **8v^2**-60v+112 : A is 8v- the leading coefficient -Trinomial (exponent of first term is in the middle)

1. Divide greatest common factor of all 3 coeffiecients
8v/4-60v/4+112/4 = 4(2v^2-15v+28)

2. Complete the X: AC on the top ; B on the bottom

3. Determine the 2 factors : Multiply on top ; Add on bottom (-7,-8) are the factors because -7*-8 =56 and -7-8= -15

4. Rewrite as 2 binomials with A as coefficient 4(2v-7)(2v-8)

5. Divide any greatest common factor individually if possible (2v-7) cannot be simplified because there is no common factor however (2v-8) can be divided by 2 (2v/2-8/2) : Making the expression 4(2v-7)2(v-4)

Regrouping:
Use when- -there are 4 terms in the polynomial spaced in equal intervals

**Steps:**
1) Regroup the 1st and 3rd terms and the 2nd and 4th terms

2)Divide out the the common factors and keep them

3)If the binomials in the parenthesis are the same rewrite them as a binomial

4) Factor each binomial more if possible

**Examples:**
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**Formula:**
a-b^3 (a+b) (a-b)

**Steps:**
1) Calculate the square root of perfect square

2) Divide the exponents by 2

3) Rewrite as a product of a binomial

**Examples:**
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