zeros multiplicity 21 videos

Using the Conjugate Zeros Theorem
Precalculus Polynomial and Rational Functions
How we find the zeros of a polynomial function when one imaginary zero is known.
polynomial functions quadratic functions zeros multiplicity the conjugate zeros theorem the conjugate roots theorem conjugates imaginary numbers imaginary zeros 
Finding Zeros of a Polynomial Function
Precalculus Polynomial and Rational Functions
How we find the zeros of a polynomial function in expanded form.
polynomial functions zeros factored form expanded form the factor theorem the rational roots theorem potential zeros synthetic division the reduced polynomial the quadratic formula 
Probability of Multiple Events
Precalculus Topics in Discrete Math
How to find the probability of multiple events.
probability mutually exclusive inclusive overlap 
Addition and Scalar Multiplication of Vectors
Precalculus Vectors and Parametric Equations
How to compute the sum of two vectors or the product of a scalar and a vector.
vector components horizontal component vertical component component form vector addition the zero vector scalar multiplication 
Introduction to Rational Functions
Precalculus Polynomial and Rational Functions
How to define rational functions, and how to identify their domain and zeros.
rational functions polynomials domain zeros 
Solving a Logarithmic Equation with Multiple Logs
Precalculus Exponential and Logarithmic Functions
How to solve a logarithmic equation by condensing one, or both, sides.
log equation logarithmic equation logarithmic form exponential form condense 
Pascal's Triangle
Precalculus Topics in Discrete Math
How to use Pascal's triangle.
zero product property factoring constant 
Probability of Independent Events
Precalculus Topics in Discrete Math
How to find the probability of independent events.
probability multiple events overlap 
Vector Operations in 3D
Precalculus Vectors and Parametric Equations
How to perform vector operations like addition, scalar multiplication, the dot product, and finding the magnitude, in three dimensions.
vectors components vector addition scalar multiplication the dot product the scalar product magnitude length three dimensions 
Square Matrices
Precalculus Systems of Linear Equations and Matrices
How to determine whether two matrices can be multiplied, and if so, what the dimensions of the product will be.
matrices rows columns dimension matrix multiplication 
The Identity Matrix
Precalculus Systems of Linear Equations and Matrices
How to determine the identity matrix of order n.
matrices square matrices the identity matrix matrix multiplication 
Intercepts and Asymptotes of Tangent Functions
Precalculus Trigonometric Functions
How to find the xintercepts and vertical asymptotes of the graph of y = tan(q).
sine cosine tangent zeros x intercepts vertical asymptotes 
Invertible Square Matrices and Determinants
Precalculus Systems of Linear Equations and Matrices
How to determine whether a square matrix is invertible using its determinant.
square matrices invertible determinant zero determinant inverse of a 2x2 matrix 
The Inverse of a Square Matrix
Precalculus Systems of Linear Equations and Matrices
How to determine whether two matrices are inverses.
matrices square matrices the identity matrix matrix multiplication invertible inverse matrix 
Unit Vectors
Precalculus Vectors and Parametric Equations
How to express a vector algebraically in terms of the unit vectors i and j.
unit vectors length magnitude the unit vectors i and j vector addition scalar multiplication component form 
The Vector Equation of a Line
Precalculus Vectors and Parametric Equations
How to write the vector equation of a line.
position vector direction vector vector addition scalar multiple vector equation line 
The Midpoint and Distance Formulas in 3D
Precalculus Vectors and Parametric Equations
How to derive the formula for the midpoint of a segment in three dimensions.
position vectors the vector from point a to point b the midpoint formula vector addition scalar multiplication 
Perpendicular, Parallel and Skew Lines in Space
Precalculus Vectors and Parametric Equations
How to determine whether two lines in space are parallel or perpendicular.
perpendicular lines dot product direction vectors parallel lines scalar multiple skew lines 
The Angle Between Planes
Precalculus Vectors and Parametric Equations
How to find the angle between planes, and how to determine if two planes are parallel or perpendicular.
normal vector the angle between planes perpendicular planes dot product scalar multiple parallel planes 
Solving Linear Systems Using Matrix Algebra
Precalculus Systems of Linear Equations and Matrices
How to convert a system of linear equations into a matrix equation and solve it.
matrices square matrices matrix equation coefficient matrix inverse matrix identity matrix matrix multiplication