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

Mathematical statements are unambiguous- nature of math, Mathematical State...

Mathematical Statements Are Unambiguous :  Consider any mathematical concept that you're familiar with, say, a sphere. The definition of a sphere is clear and precise. Given any o

Pre calc, - Find the total surface area of a frustum of a cone. (Include to...

- Find the total surface area of a frustum of a cone. (Include top and bottom). The equation that I have for volume is v=1/3 pi x h(r^2+rR+R^2) -the equation that I have found fo

Parabola, write the equation of parabola of vertex(2,-3)and focus(_1,1)

write the equation of parabola of vertex(2,-3)and focus(_1,1)

Scale Drawing, Model of 180 meter tall building using a scale of 1.5 centim...

Model of 180 meter tall building using a scale of 1.5 centimeters = 3.5 meters. How tall will the model be?

Algebraic word problems, Algebraic Word Problems: Equations: 1....

Algebraic Word Problems: Equations: 1. The total electrical output of one nuclear facility is 200 megawatts more than that of another nuclear facility. Let L be the

Fractions and equations and illustration, if Mr.Ibias oredered a rectangula...

if Mr.Ibias oredered a rectangular pizza and he wants 2/3 of the pizza to be pepperoni and 1/2 of the pizza with pineapple draw and label the pizza with toppings explain your think

Which of the following could be the dimensions the courty x, Katie's school...

Katie's school has a rectangular courtyard whose area can be expressed as 3x 2 - 7x + 2. Which of the following could be the dimensions of the courtyard in terms of x? Since t

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