5.1 - 5.2
A real number, a variable, or a product of a real number and one or more variables with whole-number exponents. Ex. - 5x
What is a monomial?
Simplifies the long-division process for dividing by a linear expression x - a. To use ____, write the coefficients (including zeros) of the polynomial in standard form. Omit all variables and exponents. For the divisor, reverse the sign (use a). This allows you to add instead of subtract throughout the process.
What is synthetic division?
The largest exponent of a polynomial represents the number of roots.
What is the Fundamental Theorem of Algebra?
a. Standard form of a parabola.
b. Vertex form of a parabola
a. What is f(x) = ax2 + bx + c?
b. What is f(x) = a(x-h)2 + h
A set of two or more equations.
A monomial or a sum of monomials. Ex. - 5x2 - 4x + 3
What is a polynomial?
a3 + b3 = (a+b) (a2 - ab + b2)
a3 - b3 = (a-b) (a2 + ab + b2)
What is a sum or difference of cubes?
A triangular array of numbers in which the first and last number of each row is 1. Each of the other numbers in the row is the sum of the two numbers above it.
What is Pascal's Triangle?
a. a line that divides the parabola into two mirror images.
b. the intersection of the parabola and its axis of symmetry; the maximum or minimum point.
a. what is the axis of symmetry?
b. what is the vertex?
TWO EQUATIONS TWO UNKNOWNS WHAT ARE OUR OPTIONS?!
What are substitute and eliminate?
Arranges the terms by degree in descending numerical order.
What is the standard form of a polynomial function?
A quick way to find the remainder of a polynomial long-division problem; if you divide a polynomial P(x) of a degree of n > 1 by x - a, then the remainder is P(a).
What is the Remainder Theorem?
A model that continually rises; represented by y=x
What is a linear model?
What is a line?
Rewriting an expression as a product of its factors.
What is factoring?
x = -b+√b2 - 4(a)(c)/2(a)
What is the quadratic formula?
a. places where the graph changes direction.
b. the directions of the graph to the far left and to the far right.
a. What are turning points?
b. What is end behavior?
You take the factors of your constant term, divide them by the factors of the leading coefficient to find the roots or use for synthetic division (will only show rational roots)
What is the Rational Root Theorem?
The graph of a quadratic function; a model represented by y=x2
What is a parabola?
Where the graph of a function crosses the x-axis.
What are zeros?
What are roots?
What are x's?
What are the solutions?
A rectangular display of numbers displayed within brackets (really nice to do on a calculator).
What is a matrix?
Describes the relationship between the linear factors of a polynomial and the zeros of a polynomial; the expression x - a is a factor of a polynomial if and only if the value a is a zero of the related polynomial function.
What is the Factor Theorem?
the number of real positive roots of a polynomial is either equal to the number of sign changes between between the consecutive coefficients, or is less than that by an even number; when you replace all the x's with -x in the same polynomial and then count the sign changes, the same is true for the real negative roots
What is Descartes' Rule of Signs?
A model represented by y=x3
What is a cubic function/model?
What is a squiggly?
A trinomial that is the square of a binomial.
Ex. x2 + 10x + 25 = (x+5)2
What is a perfect square trinomial?
When you...
1. Rewrite the equation in the form x2 + bx = c and make the coefficient of x 1.
2. add (b/2)2 to both
3. factor
4. find square roots
5. solve for x
What is completing the square?