1 year, 6 months ago
via math-questions.com
What method of factoring a polynomial is the easiest and why?
Completing the square and quadratic formula are two methods. The quadratic formula was always the easiest since you just need to know the leading coefficient of the squared term, linear term and contstant and substitute those into the formula.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$1 Answer
The easiest method of factoring depends on the equation and the person doing the factoring. What is easy for some is not always easy for others. I work with student all the time as a math tutor and many do not like completing the square and find using the quadratic formula easier. The first method students use is the "reverse FOIL" method.
Take an equation such as x^2+6x+5=0, for example.
When factoring using the reserve FOIL method you want to set up two sets of parentheses, each will have two terms and either a plus or minus separating the terms. The first in each parentheses multiply to the first term (x^2 in this case), the second numbers multiply to the last term (5 in this case) and add to the number of the middle term (6 in this case).
(x+5)(x+1)=0 is the factored form, as it meets all the criteria above. The solution is then x= -5 and x= -1
Some problems can't be factored easily in this manner, such as x^2+2x+4=0, in which case you can use quadratic formula. Think of the equation in the form ax^2+bx+c=0. In this case, a=1, b=2 and c=4
The formula is x= {-b +/- square root (b^2-4ac)}/2a. Then you just substitute the numbers into the formula. When doing so you get {-2 +/- square root(-12)}/2.. This will simplify to give you a number +/- an imaginary root. But one can see the method involved in factoring this way.
Completing the square involves isolating all the x terms on the left side of the equation with the numbers on the right. The leading coefficient of the x^2 term must be one. Then take half of the coefficient of the x term, square it and add it to both sides of the equation. From there you factor the left side of the equation in reverse FOIL form, then solve for x from there. It can be quite a bit more tricky than other methods.
Take an equation such as x^2+6x+5=0, for example.
When factoring using the reserve FOIL method you want to set up two sets of parentheses, each will have two terms and either a plus or minus separating the terms. The first in each parentheses multiply to the first term (x^2 in this case), the second numbers multiply to the last term (5 in this case) and add to the number of the middle term (6 in this case).
(x+5)(x+1)=0 is the factored form, as it meets all the criteria above. The solution is then x= -5 and x= -1
Some problems can't be factored easily in this manner, such as x^2+2x+4=0, in which case you can use quadratic formula. Think of the equation in the form ax^2+bx+c=0. In this case, a=1, b=2 and c=4
The formula is x= {-b +/- square root (b^2-4ac)}/2a. Then you just substitute the numbers into the formula. When doing so you get {-2 +/- square root(-12)}/2.. This will simplify to give you a number +/- an imaginary root. But one can see the method involved in factoring this way.
Completing the square involves isolating all the x terms on the left side of the equation with the numbers on the right. The leading coefficient of the x^2 term must be one. Then take half of the coefficient of the x term, square it and add it to both sides of the equation. From there you factor the left side of the equation in reverse FOIL form, then solve for x from there. It can be quite a bit more tricky than other methods.
images:
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$Report Abuse
