Example of factoring quadratic polynomials, Mathematics

Factor following polynomials.

                              x2 + 2x -15

Solution

x2 +2x -15

Okay since the first term is x2 we know that the factoring has to take the form.

x2 + 2 x -15 = ( x + _  )( x + _  )

We know that it will take this form as while we multiply the two linear terms the first term has to be x2 and the only way to get that is to multiply x by x. thus, the first term in each factor has to be an x. To finish this we just have to determine the two numbers that has to go in the blank spots.

We can narrow down the possibilities significantly.  Upon multiplying the two factors out these two numbers will have to multiply out to get -15.  In other terms these two numbers has to be factors of -15.  Here are all of the possible ways to factor -15 via only integers.

                       ( -1)(15)           (1) (-15)          ( -3) (5)           (3) ( -5)

Now, we can only plug these in one after another & multiply out till we get the exact pair. Though, there is another trick which we can use here to help us out. The accurate pair of numbers has to add to get the coefficient of the x term.  Thus, in this case the third pair of factors will add to "+2" & so that is the pair we are after.

Following is the factored form of the polynomial.

                                            x2 + 2 x -15 = ( x - 3) ( x + 5)

Again, we can always verify that we got the right answer my doing a quick multiplication.

Note that the method we utilized here will only work if the coefficient of the x2 term is one.  If it is anything else it won't work and we actually will be back to trial & error to get the accurate factoring form.

Posted Date: 4/6/2013 2:40:44 AM | Location : United States







Related Discussions:- Example of factoring quadratic polynomials, Assignment Help, Ask Question on Example of factoring quadratic polynomials, Get Answer, Expert's Help, Example of factoring quadratic polynomials Discussions

Write discussion on Example of factoring quadratic polynomials
Your posts are moderated
Related Questions
How to solve this: log x(81) = 4

what is the difference between North America''s part of the total population and Africa''s part

how do we solve multiple optimal solution


find the diameter of circle whose circumference is 26.51

A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of 40% acid solution.

if you have 1/5 of a candy bar and 4 friends how much will they get

Q. What is Box-and-Whisker Plot? Ans. Line graphs or stem-and-leaf plots become difficult to manage when there is a large amount of data. Box-and-whisker plots help summa

Q. Difference between Probability and statistics? Ans. Probability and statistics are used in many different aspects of life. What are they and why are they so popular?

Find the number of square feet of pavement required for the shaded portion of the streets shown in the figure, all the streets being 50 feet wide.