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

3D Trigometry problems, I have difficuties in working out those 3D trigomen...

I have difficuties in working out those 3D trigomentry problems within teh shortest possible time. Are there any tricks to get through such problems as soon as possible?

Twelve coworkers go out how many slices will each person get, Twelve cowork...

Twelve coworkers go out for lunch together and sequence three pizzas. Each pizza is cut within eight slices. If each person gets the similar number of slices, how many slices will

Properties of relations in a set, Reflexive Relations: R is a reflexive...

Reflexive Relations: R is a reflexive relation if (a, a) € R,  a € A. It could be noticed if there is at least one member a € A like (a, a) € R, then R is not reflexive. Sy

Independent & Dependent functions, I am learning this at school today and I...

I am learning this at school today and I started getting confused which one is which, can you help me?

Subtangents & subnormals, show that the subtangent at any point on parabola...

show that the subtangent at any point on parabola y2 =4ax is twice the abscissa at that point.

Calculate values of kinetics , A reaction following first-order kinetics wa...

A reaction following first-order kinetics was studied by determining the reactant concentrations at equal time intervals. Each successive pair of concentrations, [A] o and [A] 1

Differential equation and laplace transform, 1. Solve the given differentia...

1. Solve the given differential equation, subject to the initial conditions: . x2y''-3xy'+4y = 0 . y(1) = 5, y'(1) = 3 2. Find two linearly independent power series soluti

Calculus, how to find relative extrema at the indicated interval of the fol...

how to find relative extrema at the indicated interval of the following functions and how to sketch it?

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