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

Question, Hi I have a maths question related to construction as its a cons...

Hi I have a maths question related to construction as its a construction management course...i could send some example sheets too...could it be done?

Congruence of triangle, make an assignment based on congruence of triangle

make an assignment based on congruence of triangle

Volume of grains in the silo , The volume of grains in a silo at a particul...

The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m 3 . Find the rate of change of the volume of grains in the silo from first pri

Quantitative Technique in Marketing, a company''s advertising expenditures ...

a company''s advertising expenditures average $5,000 per month. Current sales are $29,000 and the saturation sales level is estimated at $42,000. The sales-response constant is $2,

Geometry of convex sets, (a) Given a norm jj jj on Rn, express the closed b...

(a) Given a norm jj jj on Rn, express the closed ball in Rn of radius r with center c as a set. (b) Given a set A and a vector v, all contained in Rn, express the translate of A by

Fermats theorem, Fermat's Theorem  If f(x) has a relative extrema at x...

Fermat's Theorem  If f(x) has a relative extrema at x = c and f′(c) exists then x = c is a critical point of f(x). Actually, this will be a critical point that f′(c) =0.

Compute standard and variance deviation, A firm is manufacturing 45,000 uni...

A firm is manufacturing 45,000 units of nuts. The probability of having a defective nut is 0.15 Compute the given i. The expected no. of defective nuts ii. The standard an

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