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

Calculus, The law of cosines can only be applied to acute triangles. Is thi...

The law of cosines can only be applied to acute triangles. Is this true or false?

Constant aceleration formulae, a car comes to a stop from a speed of 30m/s ...

a car comes to a stop from a speed of 30m/s in a distance of 804m. The driver brakes so as to produce a decelration of 1/2m per sec sqaured to begin withand then brakes harder to p

Explain introduction to non-euclidean geometry, Explain Introduction to Non...

Explain Introduction to Non-Euclidean Geometry? Up to this point, the type of geometry we have been studying is known as Euclidean geometry. It is based on the studies of the a

find out the dimensions which will minimize, We desire to construct a box ...

We desire to construct a box whose base length is three times the base width. The material utilized to build the top & bottom cost $10/ft 2 and the material utilized to build the

Differential equation.., 3.6Find the general solution of the differential e...

3.6Find the general solution of the differential equation Y" + 4y = Sec2 2x

Explain the common forms of linear equations, Explain the Common Forms of L...

Explain the Common Forms of Linear Equations ? An equation whose graph is a line is called a linear equation. Here are listed some special forms of linear equations. Why should

Are parrellel meet at infinity?, no the parallel lines do not meet at infin...

no the parallel lines do not meet at infinity because the parallel lines never intersect each other even at infinity.if the intersect then it is called perpendicuar lines

Ratio, 2qt :6qt::x :48? help me solve x

2qt :6qt::x :48? help me solve x

Integers, what are 20 integer equations that have multiplication, division,...

what are 20 integer equations that have multiplication, division, subtraction,and additon??

Greens function, construct the green''s function that satisfies dG''''-(2x+...

construct the green''s function that satisfies dG''''-(2x+1)G''+(x+1)G=delta(x-s), G(0,s)=G(1,s)=0

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