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

Functions of limits, Following is some more common functions that are "nice...

Following is some more common functions that are "nice enough". Polynomials are nice enough for all x's. If f ( x) = p ( x ) /q (x ) then f(x) will be nice enough provid

Point of intersection, Equation of line joining(0,0)and point of intersecti...

Equation of line joining(0,0)and point of intersection of X2+Y2+2XY=4 , 3x2+5y2-xy=7 is solution) The two equations above represent pair of straight lines. We can complete the sq

Calculus, f(x)= 2e^5x+6 find the domain of f and find x-intercept.

f(x)= 2e^5x+6 find the domain of f and find x-intercept.

Solve step by step, Use an appropriate infinite series method about x = 0 t...

Use an appropriate infinite series method about x = 0 to find two solutions of the given differential equation: y''''-xy''-y=0

Gauss-siedel or newton-rapson method, A one-line diagram of a simple three-...

A one-line diagram of a simple three-bus power system is shown in Figure 1 with generation at bus 1. The magnitude of voltage at bus 1 is adjusted to 1.05 per unit. The scheduled l

Partial Differentiation, If the sides angles of a triangle ABC vary in such...

If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0

Shares and dividend, by purchasing rs.10 shares for rs.40 each mala gets 5%...

by purchasing rs.10 shares for rs.40 each mala gets 5% income on her investment. what rate of dividend is the company paying? what will be the amount of dividend if she buys 120 sh

6th grade, what is the length of a line segment with endpoints (-3,2) and (...

what is the length of a line segment with endpoints (-3,2) and (7,2)?

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