Purchase Solution

Proof : Polynomials

Not what you're looking for?

Ask Custom Question

Problem:
Let f(x) and g(x) be nonzero polynomials in R[x] and assume that the leading coefficient of one of them is a unit. Show that f(x)g(x) doesn't equal 0 and that deg[f(x)g(x)] = deg(f(x)) + deg(g(x))

Purchase this Solution

Solution Summary

A polynomial proof is provided.

Solution Preview

Proof:
Without the loss of generality, we suppose the leading coefficient of f(x) is a unit. We can suppose f(x)=anx^n+...+a1x+a0, g(x)=bmx^m+...+b1x+b0, where ...

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts