Polynomial
an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
Polynomial function
where are real numbers and n is a nonnegative integer
Standard form
written down in the way most commonly accepted" It depends on the subject
Degree of term
when the polynomial is expressed in its canonical form consisting of a linear combination of monomials
Monomial
an algebraic expression consisting of one term.
Binomial
an algebraic expression of the sum or the difference of two terms.
Trinomial
(of an algebraic expression) consisting of three terms.
Degree of a polynomial
the highest degree of its terms when the polynomial is expressed in its canonical form consisting of a linear combination of monomials
Leading term
highest degree in a given polynomial
Leading coefficient
the numbers written in front of the variable with the largest exponent.
Adding polynomials
just a matter of combining like terms, with some order of operations considerations thrown in
Subtracting polynomials
quite similar to adding polynomials, but you have that pesky minus sign to deal with
Multiplying a monomial and a polynomial that is
not a monomial
the product of one or more constants and variables
FOIL
A technique for distributing two binomials
The product of the sum and difference of two
terms
When distributing binomials over other terms, knowing how to find the sum and difference of the same two terms is a handy shortcut. The sum of any two terms multiplied by the difference of the same two terms is easy to find and even easier to work out � t
The square of a Binomial sum
equal to the square of the first term, plus the double of the product of the first by the second plus the square of the second term.
The square of a binomial difference
equal to the square of the first term, minus the double of the product of the first by the second plus the square of the second term.
Factoring over the set of integers
where n (the number of roots or factors) is the degree of the
polynomial, a is the leading coefficient (coefficient of x^n), and r1
through rn are the n complex roots
Irreducible over the integers
a non-constant polynomial that cannot be factored into the product of two non-constant polynomials
Prime
can be divided evenly only by 1, or itself.
And it must be a whole number greater than 1
Greatest common factor
the greatest factor that divides two numbers. To find the GCF of two numbers: List the prime factors of each number
Factoring a monomial from a polynomial
both polynomials have more than one term you just multiply each of terms in the first polynomial with all of the terms in the second polynomial
Factoring by grouping
one way to factor a polynomial,take a polynomial and factor it into the product of two binomials
The difference of two squares
when the numerical coefficient (the number in front of the variables) is a perfect square and the exponents of each of the variables are even numbers
Factoring perfect square trinomials
when factored gives you the square of a binomial.
Factoring a polynomial
he opposite process of multiplying polynomials
Quadratic equation
as an equation of degree 2, meaning that the highest exponent of this function is 2
The zero-product principle
Solve equations using the principle of zero products. " Solve quadratic equations by factoring and then using the principle of zero products.
Solving a quadratic equation by factoring
Factoring quadratics finds the roots or x-intercepts of a quadratic equation. Factoring quadratic equations in standard form, , can often be accomplished by finding two numbers that add to give b, and multiply to give ac
The square root property
one method that is used to find the solutions to a quadratic (second degree) equation. This method involves taking the square roots of both sides of the equation
Quadratic formula
used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with
Projectiles
A formula used to model the vertical motion of an object that is dropped, thrown straight up, or thrown straight down
Quadratic function
a second-degree polynomial function of the form , where a, b, and c are real numbers and . Every quadratic function has a "u-shaped" graph called a parabola.
Parabola
a fixed point (the focus), and ...
... a fixed straight line (the directrix)
Vertex
each angular point of a polygon, polyhedron, or other figure
Axis of symmetry
the vertical line that goes through the vertex of a quadratic equation
The vertex of a parabola
is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the "U"-shape.
Finding the parabola's x-intercepts
The x-intercepts are the points or the point at which the parabola intersects the x-axis. A parabola can have either 2,1 or zero real x intercepts.
Graphing a quadratic function
graph of a quadratic function is a parabola. The standard form of a quadratic function is written as . If , the parabola opens upward; if , it opens downward