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
Mike can jog 6.5 miles per hour. At this rate, how many miles will he jog in 30 minutes? Thirty minutes is half an hour. Thus, divide the number of miles Mike can jog in one ho


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

a shopkeeper buys two cameras at the same price . he sells one camera at a profit of 18% and the other at a price of 10% less than the selling price of the first camera. find his p

help solve these type equations.-4.1x=-4x+4.5



Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections.  Two vectors are parallel if they have

a company of 10000 shares of rs 100 each declares a annual dividend of 5 %.what is the total amount dividend paid by the company

the number is 605176 the underline digit is 0