Multiplication of polynomials and evaluating expressions

1. How would you teach the multiplication of polynomials?

2. What four steps should be used in evaluating expressions? Could these steps be skipped or rearranged? Explain your answersr.

3. Do you always use the property of distribution when multiplying monomials and polynomials? Explain why or why not. Also what type of situations would distribution become important?

Solution Preview

1) Multiplication of polynomials is VERY similar to multiplication of whole numbers. Take, for example, a simple one:

111x77

You would write the problem like this

111
x77
-----
777
+7770

So what you have done is broken it up into several addition steps. We can do the exact same with polynomials:

Take (x^2+2x+7)*(x+2)

Arrange it exactly the same!
x^2+2x+7
x+2

Now generate addition steps. We go from right to left, just like in the multiplication of whole numbers. Start by multiplying 2 to (x^2+2x+7)

This solution answers the three questions posed by the original student, so the solution itself seeks to explain these processes in as much detail as possible. It is approached from the perspective of helping a parent teach their child the math, so it is presented in solution form in as simple a manner as possible, creating a thorough set of rules and hints for solving the multiplication of polynomials and using order of operations. Also, we answer the question, "Why do we use the FOIL method when multiplying binomials?" This solution is a real tour de force!

Please explain as simple as possible how multiplicationand division of rational expressions can be done. Please show examples of each in simple form by typing out linearly and use parentheses around top and bottom if there's more than 1 term.

(1) Explain how multiplying and dividing rational expressions is similar to multiplicationand division of fractions. Give an example of each and compare the process.
(2) When simplifying the rational expression (x+8)/(x+2), explain why it is improper to cancel out the x's. State a general rule for canceling factors in a rati

Using the fact that 1+x = 4+(x-3), find the Taylor series about 3 for g. Give explicitly the numbers of terms. When g(x)=square root of 1+x
Check the first four terms in the Taylor series above and use these to find cubic Taylor polynomials about 3 for g.
Use multiplication of Taylor series to find the quartic Taylor polyn

Is the multiplication of complex numbers similar to multiplication of polynomials? Is it possible to apply the FOIL method when multiplying complex numbers? Explain your answers.

Imagine your younger relative, of middle school age, was taking an algebra course and asked for your help, how would you teach the multiplication of polynomials to him/her?

I would like help understanding why it is important to simplify radicals expressions before adding and subtracting? How is adding radicals expressions similar to adding polynomialsexpressions? How is it different? also, an example of an radical expression would be great? I'm having hard time finding comprehensive information.

Design and implement a class for dealing with polynomials. The polynomial
a(n)x^n + a(n-1)x^(n-1) + . . . + a0
will be implemented as a linked list. Each node will contain and int value for the power of x and an int value for the corresponding coefficient. The polynomial operations should include addition, multiplication, an

1. For each polynomial listed below, determine
i the degree of the polynomial
ii the coefficient of the leading term
iii the constant term
a. P(x) = x + 1
b. Q(x) = 3x + 2
c. R(x) = x2 + 2x + 1
d. W(x) = 4x2 + x + 3
e. Z(x) = 3x3 + 2x2 + x

It is important to simplify radical expressions before adding or subtracting to get terms with like radicals. Once we find terms with like radicals we can then add or subtract the expressions. Simplifying the expression and obtaining terms with like radicals makes the problem less complex when solving. We can follow the same rul