Method to solve binomials of second degree, Mathematics

Assignment Help:

In this part we look at another method to obtain the factors of an expression. In the above you have seen that x2 - 4x + 4 = (x - 2)2 or (x - 2)(x - 2). If you observe it carefully we find that the middle number - 4 is the sum of -2 and -2 and the last term 4 is the product of -2 and -2. That is, if you think that so and so number might be the factors of the binomial those numbers should satisfy this condition. We take another example. You are given x2 + 15x + 56 and asked to factorize it. Now if you think that, say, 6 and 7 are the factors of this expression then their product should be equal to 56 and their sum should be equal to 15. However in this case we observe that the product is 42 and the sum is 13. Therefore, 6 and 7 cannot be the factors of this expression. Now try 7 and 8. We find that their product is 56 and the sum 15. That is, 7 and 8 are the factors of the given expression. This can be clarified by multiplying (x + 8) and (x + 7).

One point to which we have to pay attention is that we have to take even signs into consideration. For instance, consider an expression x2 - 17x + 70. What could be the factors of this expression? Let us try 7 and 10. No doubt, the product is 70 and the sum 17. Still these cannot be the factors of the given expression, because the sum is -17 and we got only 17. Now let us try -7 and -10. The sum of these two numbers gives us -17 and their product as 70. This is what we require. Therefore, the factors are x - 7 and x - 10 (observe that in this case if we took x = -7 and         x = -10, we would have got the factors as x + 7 and x + 10, whose multiplication would give us x2 + 17x + 70 and not x2 - 17x + 70. That is, the values should be considered as they are). Now let us consider an expression x2 - 3x - 70. Let us try 7 and -10 for this expression. The sum of these two values is -10 + 7  = -3 and the product being -70. That is, x + 7 and x - 10 are two factors of the given expression and not x - 7 and x + 10.


Related Discussions:- Method to solve binomials of second degree

Trigonometry, what are reason inside a circle?

what are reason inside a circle?

Interpretation of the second derivative, Interpretation of the second deriv...

Interpretation of the second derivative : Now that we've discover some higher order derivatives we have to probably talk regarding an interpretation of the second derivative. I

Cartesian product of sets, The Cartesian product (also called as the cross ...

The Cartesian product (also called as the cross product) of two sets A and B, shown by AΧB (in the similar order) is the set of all ordered pairs (x, y) such that x€A and y€B. What

Prepare a bar diagram, Question Write a short note on the following: ...

Question Write a short note on the following: 1 The weekly salaries of a group of employees are given in the following table. Find the mean and standard deviation of the

Find the limit of given matrix, What is required: This assignment is to be ...

What is required: This assignment is to be resolved using Maple. You are to upload a single Maple worksheet with file name FamilynameFirstname.mw (e.g., CarrElliot.mw), using the A

Differential equation to determine initial value problem, Solve the subsequ...

Solve the subsequent IVP. cos(x) y' + sin(x) y = 2 cos 3 (x) sin(x) - 1 y(p/4) = 3√2, 0 Solution : Rewrite the differential equation to determine the coefficient of t

Which a dog is their favorite type of pet, The students at Norton School we...

The students at Norton School were asked to name their favorite type of pet. Of the 430 students surveyed, 258 said in that their favorite type of pet was a dog. Assume that only 1

Calculate the value of expected value, The owner of TMH Hospital wants to o...

The owner of TMH Hospital wants to open a new facility in a certain area. He usually builds 25-, 50-, or 100-bed facilities, depending on whether anticipated demand is low, medium

Detemine multiplying a polynomial by a monomial, Detemine Multiplying a Pol...

Detemine Multiplying a Polynomial by a Monomial? To multiply a polynomial by a monomial, use the distributive property. Let's start by talking about ordinary numbers. Say th

Creating input- output tables, How do I create an input-output table with t...

How do I create an input-output table with the rule -12

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd