Unit 6: Alegbra II

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horizontal line test

If every horizontal line intersects a graph of a function just once, then the function is one-to-one and therefore an inverse function exists.

vertical line test

If every vertical line intersects a graph just once, the graph is of a function.

The triangle of numbers used to find the pattern for any power of binomials is called ___ Triangle.

Pascal's

synthetic division

a shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomials

Pascal's Triangle

a triangular array of numbers such that each row is the coefficients of the terms of the expanded form of the powers of a binomial of the form (a+b)N

root of a polynomial

a value for the variable of a polynomial that makes the polynomial equal to zero

If the highest exponent of a polynomial function is odd, then the range of the function is ____ all real numbers.

always

The domain of a polynomial function is ____ all real numbers.

always

The set of polynomials is ___ closed under multiplication.

always

If the monomial is not zero, the product of a monomial and a polynomial will have ___ the polynomial.

as many terms as

In most cases, the product of a monomial and a binomial is a ___

binomial

In most cases, the product of a monomial and a binomial is a ___.

binomial

The coefficients of the terms on the right side of a ___ equation are the numbers in Pascal's Triangle.

binomial

The numerators of any rational roots of a polynomial will be factors of the ___.

constant term

Multiplying polynomials is done by applying the ___ Property when necessary.

distrubutive

To find the roots of a polynomial, it is often useful to find the ____ of the polynomial.

factors

The denominators of any rational roots of a polynomial will be factors of the ____.

leading coefficient

If the highest exponent of a polynomial function is even, then the range of the function is ____ all real numbers.

never

If the leading coefficient of a polynomial function is positive, then the right end of the graph ____ points down.

never

The set of polynomials is ___ closed under division

not

The set of polynomials is ___ closed under division.

not

A constant is a real ___.

number

A linear function, in the form f(x)=mx+b is a ___ function

polynomial

Closure means that whenever you add or subtract two polynomials, you get a ____.

polynomial

The composition of a polynomial function and another polynomial function will be a ___ function

polynomial

A term is a constant, a variable, or a ___ of numbers and variables.

product

Quotients of polynomials are called ___ expressions.

rational

A variable is a letter that stands for a(n) ___ number.

real

_____ number roots of a polynomial are the points where the graph of the related polynomial function crosses the x -axis

real

If the leading coefficient of a polynomial function is negative, then the left end of the graph ____ points down.

sometimes

The range of a polynomial function is ____ all real numbers

sometimes

Each number in Pascal's Triangle is the ___ of the two numbers directly above it in the previous row.

sum

A shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomial is called ___.

synthetic division

The value of a polynomial at x=1 is the remainder when the polynomial is divided by ____.

x-1

Roots of a polynomial are the values that make the polynomial equal to ___.

zero


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