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Math 11

SLS - Math 11 - Ch 4- Quadratic & Polynomial Equations

QuestionDefinition
Remainder Theorem When a polynomial P(x) is divided by x-b, the remainder is P(b). ie, replace x with b and simplify.
Factor Theorem When x-b is a factor of the polynomial P(x), P(b)=0
The discriminant of a quadratic equation is negative in this case When there are no real solutions (only imaginary solutions).
The discriminant of a quadratic equation is zero in this case When there are two equal real solutions (looks like one solution).
The discriminant of a quadratic equation is positive in this case When there are two distinct real solutions.
What are 3 methods of solving a quadratic equation? any 3 of: graphing, factoring, the square root principle, the quadratic formula, or completing the square
Describe how to solve a quadratic by graphing. Move all terms to one side. Input in calculator. Find x intercepts.
Two other names for a "root" of a quadratic equation are: Any 2 of: zero of the graph, x intercept of the graph, solution
Describe how to solve a quadratic by factoring. Move all terms to one side, simplify and write in descending order. Factor. If factors are (2x-5)(x+4) the solutions are 5/2 and -4.
Describe how to solve a quadratic with the square root principle. There must be an x^2 term and a constant. No x term or other terms. Move the x^2 term to one side and the constant to the other. Square root both sides, with +- on the root. Reduce the radical. Isolate x.
Describe how to solve a quadratic with the quadratic formula. Move all terms to one side, simplify and write in descending order. Plug coefficients into the quadratic formula. Simplify the positive and negative answers separately.
List three types of polynomials by degree. Any 3 of: Linear, Quadratic, Cubic, Quartic, Quintic.
List 2 types of polynomials by number of terms. Any three of: monomial, binomial, trinomial (and the general description polynomial)
The Rational Zero Theorem The possible rational zeros of a polynomial are the factors of the constant term divided by the factors of the leading coefficient.
Describe the graphical method to solve a polynomial equation (other than a quadratic). Move all terms to one side. Graph and find the zeros.
Describe the algebraic method for solving a polynomial of degree 3 or more. Use the rational root theorem, factor theorem, and synthetic division until a quadratic remains. Factor it.
Created by: slscarrie