Method to solve binomials of second degree, Mathematics

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.

Posted Date: 9/13/2012 3:42:52 AM | Location : United States







Related Discussions:- Method to solve binomials of second degree, Assignment Help, Ask Question on Method to solve binomials of second degree, Get Answer, Expert's Help, Method to solve binomials of second degree Discussions

Write discussion on Method to solve binomials of second degree
Your posts are moderated
Related Questions
Product Moment Coefficient This gives an indication of the strength of the linear relationship among two variables. Note that this formula can be rearranged to have di

darien agrees to sponsor her sister $8 plus $1 for every mile she walks.Write an expression to show her total money

You are painting the surface of a silo that has a diameter of 16 ft and height of 50 ft. What is the net surface area to be painted? Consider the top of the silo is  1/2 a sphere

(b) The arity of an operator in propositional logic is the number of propositional variables that it acts on – for example, binary operations (e.g, AND, OR, XOR…) act on two propo

Ask question #Min 4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

Calculate the Kendaul''s correlation cofficient for a given data.

how to describe the locus of the equation x^2+6xy+y^2+z^2=1 in cylindrical polar coordinates?

particular solution of equation y''''-3y''-4y=2sinx

From  an  aero  plane  vertically  above  a  straight  horizontal  road,  the  angles  of depression of two consecutive milestones on opposite sides of the aero plane are observed

If the radius of a sphere is doubled, the surface area is a. multiplied by 4. b. multiplied by 2. c. multiplied by 3. d. multiplied by 8. a. The formula for the surf