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

1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is di erent

Calculus with Matrices There actually isn't a whole lot to it other than to just ensure that we can deal along with calculus with matrices. Firstly, to this point we've onl

in a veggie mix the ratio of cups of carrots to cups of broccolie is 4 to 5 if you made this party mix larger how many cups of carrots would be needed to mix with fo cups of brocco


Relative measures of dispersion Definition of Relative measures of dispersion: A relative measure of dispersion is a statistical value that may be utilized to compare va

Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp

On dividing the polynomial 4x 4 - 5x 3 - 39x 2 - 46x - 2 by the polynomial g(x) the quotient is x 2 - 3x - 5 and the remainder is -5x + 8.Find the polynomial g(x). (Ans:4 x 2 +

How do you reflect about the origin

1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n