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GCF of a List of Common Variables

Raised to Powers

The variable raised to the smallest exponent in the list.

### Factoring by Grouping

A technique for factoring a four-term polynomial where you group terms in two groups of two terms so that each group has a common factor, factor out the GCF of each group, and then factor out a common binomial.

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Factoring a Trinomial in the Form

x² + bx + c

The factored form is (x + #1)(x + #2),

where #1 and #2 have a product of c and a sum of b.

### Factoring a Perfect Square Trinomial

A trinomial that is the square of some binomial can be factored as follows:

a² + 2ab + b² = (a + b)²

a² - 2ab + b² = (a - b)²

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Factoring a Trinomial in the Form

ax² + bx + c

The process of trying various combinations of factors of 'ax²' and 'c' until a middle term of 'bx' is obtained when checking.

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Factoring a Trinomial in the Form

ax² + bx + c by Grouping

The process of finding two numbers whose product is 'a' times 'c' and whose sum is 'b', rewriting 'bx' using the factors found and then factoring by grouping to finish.

### Factoring a Difference of Squares

A binomial that is a difference of squares can be factored as follows:

a² - b² = (a + b)(a - b)

### Factoring the Sum of Two Cubes

A binomial that is a sum of cubes can be factored as follows:

a³ + b³ = (a + b)(a² - ab + b²)

### Factoring the Difference of Two Cubes

A binomial that is a difference of cubes can be factored as follows:

a³ - b³ = (a - b)(a² + ab + b²)

### Quadratic Equation in Standard Form

An equation that can be written in the form:

ax² + bx + c = 0

where a, b, and c are real numbers and a ≠ 0.

### Factoring a Quadratic Equation

The process of writing an equation in standard form so that one side of the equation is 0, factoring the quadratic, setting each factor containing a variable equal to 0 and solving.

### Quotient Rule for Radicals

If √a and √b are real numbers and b ≠ 0,

then √(a / b) = √a / √b, for any index

### Rationalizing the Denominator

The process of eliminating the radical in the denominator of a radical expression

### Conjugate

Used to rationalize a denominator for a sum or difference of radicals. The sign in between becomes the opposite (addition to subtraction, or subtraction to addition). For example, a + b becomes a - b.

### Pythagorean Theorem

If a and b are lengths of the legs of a right triangle and c is the length of the hypotenuse, then a² + b² = c².

### Distance Formula

The distance d between two points with coordinates

( x₁, y₁) and ( x₂, y₂) is given by

d = √( x₂ - x₁)² + ( y₂ - y₁)².

### Polynomial

A finite sum of terms of the form ax^n, where a is a real number and n is a whole number.

### Degree of a Polynomial

The greatest exponent of any term of the polynomial. Determines how many times the polynomial could cross the x-axis.

### Dividing by a Monomial

Divide each term of the polynomial in the numerator by the monomial: (a + b + c)/d = a/d + b/d + c/d.

### Synthetic Division

Able to use in division polynomial problems when the divisior is a linear binomial.

### Scientific Notation

A positive number is written as a product of a number 'a', where 1≤ a <10, and an integer of power 'r' of 10:

a x 10^r.