# Assignment: Pre-Cal Problems

Assignment: Pre-Cal Problems

Assignment: Pre-Cal Problems

Use the remainder theorem and synthetic division to find f(k)

K=-1;f(x)=x2-4x+5

F(k)=

Use the remainder theorem and synthetic division to find f(k) for the given value of k.

F(x) = -x3-10×2-25x-13;k=-6

F(-6)=

Use the remainder theorem and synthetic division to find f(k) for the given value of k.

F(x)=3×4-17×3-3×2+4x+4;k=-1/3

F(-1/3)=

Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value off(k).

F(x)=x2-8x+15;k=5

Is 5 a zero of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

For the polynomial function, use the remainder theorem and synthetic division to find f(k).

F(x)=3×2+48,k=4i

F(4i) =

Express f(x) in the form f(x)=(x-k)q(x)+r for the given value of k.

F(x)=x3+5×2+7x+2,k=-2

Precalculus Problems and Solutions

Precalculus topics will act as a bridge between algebra and calculus, and will include information from advanced algebra and trigonometry courses.

Precalculus is a set of concepts that are required to comprehend calculus.

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Sets A basic introduction to sets, one of mathematics most fundamental concepts.

The concept of sets introduces object grouping and numerical classifications.

Exponential Functions are a type of function that is defined as a

Exponents are extended in terms of functions, and the constant e is introduced.

Exponential growth and decay, dealing with logs, compound and continuously compounded interest, and the exponential function of e are only a few of the topics covered.

Logarithmic Functions are functions that have a logarithmic scale.

A more detailed examination of logarithms and logarithmic functions, as well as their relationship to exponents.

The standard and natural logarithms, as well as solving for x and the inverse properties of logarithms, are all covered.

Functions of Radicals

An introduction to square root and radical functions, as well as how they relate to conic sections.

Functions that locate the zeros of radical functions, functions with square roots and higher roots, and functions with no solution are some of the topics covered.

Sequences and Series

The concepts of Mathematical Patterns and how to deal with them are introduced through the use of Sequences and Series.

This section covers the many forms of Series and Sequences, as well as how to discover the next word in a sequence or the sum of a sequence.

The following are the most common types of series and sequences:

Progression in Arithmetic

Progression in Geometry

Factorials, permutations, and combinations are all types of permutations and combinations.

The factorial notation is explained.

The concept of permutations and combinations is discussed and introduced.

Theorem of Binomials

The Binomial Theorem is stated.

The relationship between Pascals Triangle and the Binomial Theorem.

The Binomial Theorem is used to expand polynomials.

Equations with Parameters

A look at how to use parametric equations, including how to parametrize functions and how to find a function for a set of them.

Parameterizing lines, segments, circles, and ellipses, as well as piecewise functions, are among the topics covered.

Coordinates of the Polar Regions

The polar coordinate system is explained.

Converting from rectangular to polar and polar to rectangular coordinates, converting degrees and radians, and polar equations are among the topics covered.

Matrices

The concept of matrices is introduced.

The various types of matrices are discussed.

Addition, subtraction, and multiplication are all part of matrix algebra.

Inverses and determinants of matrices.

There are several subpages, including:

Equality in the Matrix

Subtraction and addition of matrices

Multiplication of Matrixes

Matrices Unique

Matrix in reverse

Row Echelon Form Reduction

Equations in Systems

We come across systems of equations all the time, and were frequently stumped as to how to solve them.

Most of the time, were dealing with two- or three-variable systems of equations, but the approaches in this section can be applied to any number of variables.

The secret is to figure out which one will work best and quickly for you.

The following are some of the methods described:

Method of Substitution

Method of Elimination

Method of the Matrix

Systems that are consistent and those that are inconsistent

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