Chapter Q Vocab

Fundamental Theory of Algebra

The degree is how many answers there are.

Degree

t\The degree of a polynomial refers to the highest power of the variable in the polynomial expression that determines the number of solutions.

Prime Factorization

The process of expressing a number as a product of its prime factors. This method is essential in number theory and helps in simplifying fractions and finding the greatest common divisor.

Expression

A mathematical phrase that can include numbers, variables, and operators, but does not contain an equality sign.

If there is no equal sign…

it is not an equation; you can not solve

P.S.T

Perfect Square Trinomials

Characteristics of a P.S.T

1st and 3rd term are a perfect square, second term must be even, and the coefficient has to be even/ divisible by 2

D.O.S

Difference of Squares

Characteristics of a D.O.S

No second term, first and third terms are both perfect squares, third terms has to be negative.

Expanding

multiplying the

Trinomial

A polynomial with three terms, typically in the form ax² + bx + c.

Binomial

A polynomial with two terms, usually expressed in the form ax + b.

radical

An expression that involves the root of a number, typically represented as √x.

radican

The number or expression under a radical sign, such as in √x where x is the radican.

extraneous solution

A solution derived from an equation that is not a valid solution to the original equation

Why can you not divide by a variable?

Dividing by a variable can lead to undefined results if the variable equals zero, which invalidates the operation and can introduce extraneous solutions.

Not Factorable

Prime

You can NOT divide when things are connected by….

addition

If you divide by a variable…

then you mess with the degree, which you can not do.

If you can put a number in fraction form…

then it is a rational number