Example of factoring quadratic polynomials, Mathematics

Assignment Help:

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.


Related Discussions:- Example of factoring quadratic polynomials

Evaluate the volume of cylinder, If the diameter of a right cylinder is dou...

If the diameter of a right cylinder is doubled and the height is tripled, its volume is a. multiplied by 12. b. multiplied by 2. c. multiplied by 6 d. multiplied by 3.

Triangles, if A be the area of a right triangle and b be one of the sides c...

if A be the area of a right triangle and b be one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2Ab/rootb^4+4A^2

Unite Ratet, How does finding the unit rate help make smart decisions?

How does finding the unit rate help make smart decisions?

The sum of two integers is 36 what is the smaller number, The sum of two in...

The sum of two integers is 36, and the difference is 6. What is the smaller of the two numbers? Let x = the ?rst integer and let y = the second integer. The equation for the su

Caselets, how are indian customers visiting shoppers stop any different fro...

how are indian customers visiting shoppers stop any different from customers of developed western countries

saxon math, what is the muttiplied number of mutttiplacation calle

what is the muttiplied number of mutttiplacation called

Marketing research, Discuss the role research would play during your decisi...

Discuss the role research would play during your decision making

Linear approximation method for interpolation, Linear Approxi...

Linear Approximation Method This is a rough and ready method of interpolation and is best used when the series moves in predicted interval

Operation research, approximate the following problem as a mixed integer pr...

approximate the following problem as a mixed integer program. maximize z=e-x1+x1+(x2+1)2 subject to x12+x2 =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