Operation on polynomial, Mathematics

Perform the denoted operation for each of the following.

 (a) Add 6x5 -10x2 + x - 45 to 13x2 - 9 x + 4 . 

 (b) Subtract 5x3 - 9 x2 + x - 3 from       x2+ x +1. 

Solution

(a) Add 6x5 -10x2 + x - 45 to 13x2 - 9 x + 4 . 

The first thing which we have to do is in fact write down the operation which we are being asked to do.

                        (6 x5 -10 x2 + x - 45) +(13x2  - 9 x + 4)

In this case the parenthesis is not needed since we are going to add the two polynomials. They are there basically to make clear the operation which we are performing.  In order to add two polynomials all that we do is combine such as terms. It means that for each term with the similar exponent we will add or subtract the coefficient of that term.

In this case this is,

 (6x5 -10x2 + x - 45) + (13x2 - 9 x + 4) =6 x5 + (-10 + 13) x2 + (1 - 9) x - 45 + 4

                                                             = 6x5 + 3x2 - 8x - 41

(b) Subtract 5x3 - 9 x2 + x - 3 from x2 + x + 1.

Again, let's write down the operation we are doing here.  We will also need to be very careful with the order that we write things down in.  Here is the operation

                                                  x2 + x + 1 - (5x3  - 9 x2 + x - 3)

This time the parentheses about the second term are absolutely needed.  We are subtracting the whole polynomial & the parenthesis has to be there to ensure we are actually subtracting the whole polynomial.

In performing the subtraction the first thing which we'll do is distribute the minus sign through the parenthesis. It means that we will alter the sign on every term into the second polynomial. Notice that all we are actually doing here is multiplying a "-1" to the second polynomial via the distributive law.  After distributing the minus through the parenthesis again we combine like terms.

Here is the work for this problem.

x2 + x + 1 - (5x3  - 9 x2 +x - 3) = x2 + x + 1 - 5x3 + 9 x2 - x + 3

                                                 = -5x3 + 10x2 + 4

Notice that sometimes a term will totally drop out after combing such as terms as the x did here. It will happen on occasion thus don't get excited about it while it does happen.

Now let's move over multiplying polynomials.  Again, it's best to do these in an instance.

Posted Date: 4/6/2013 2:28:13 AM | Location : United States







Related Discussions:- Operation on polynomial, Assignment Help, Ask Question on Operation on polynomial, Get Answer, Expert's Help, Operation on polynomial Discussions

Write discussion on Operation on polynomial
Your posts are moderated
Related Questions
use the bionomial theorem to expand x+2/(2-X)(WHOLE SQUARE 2)

How to solve Brahmaguptas Problem? Explain Brahmaguptas Problem solving method?

Finding the Equation of a line, Given a Slope and a Point ? Find the equation of a line with slope m = 2, which passes through the point (-1, -3). Solution: Use the po

You have just renegotiated the interest rate of your home mortgage loan. (This is called rate modification.)  The original loan of $400,000 carries an interest rate is 6% has an or

For a first order linear differential equation the solution process is as given below: 1. Place the differential equation in the correct initial form, (1). 2. Determine the i

Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ut(x, 0) = ?(x) =1 if-1 Sketch snapshots of the solution u(x, t) at t = 0, 1, 2 with justification (Hint: Sket

a)    A palindrome is a word that reads the similar whether read from right to left or from the left to right, the word ROTOR, for example. Let  be the number of words of length n,

Illustration of Rank Correlation Coefficient In a beauty competition two assessors were asked to rank the 10 contestants by using the professional assessment skills. The resul

An advertising project manager developed the network diagram shown below for a new advertising campagign.  In addition, the manager gathered the time information for each activity,

If PA and PB are tangents to a circle from an outside point P, such that PA=10cm and ∠APB=60 o . Find the length of chord AB.