How do we know whether a quadratic equation can be factorised or whether it needs to be solved using the formu

Question

How do we know whether a quadratic equation can be factorised or whether it needs to be solved using the formula?

It's just that it seems we have to do so much work trying to work out whether or not it can be factorised that it would just be easier to use the formula every time. But then I don't understand why the text book even bothered to mention factorisation if it's not needed.

Answer 1

The sure way to solve it is to use the formula, but sometimes it is faster to use factoring.

Check out this web site:

http://www.purplemath.com/modules/solvquad.htm

Answer 2

If you know your multiplication table backwards and forwards, factoring polynomial equations should be second nature. While the Quadratic Formula is a surefire way to solve the problem, it is not necessarily the quickest and it is limited

Practically speaking, the Quadratic Formula is only useful for solving second-degree equations. By second-degree, I mean those polynomial equations that have a variable to the power of 2.
eg.
ax^2 + bx + c = 0

There are formulas to solve for the roots for up to 5th-degree equations, however there are no convenient formulas to solve for the roots of any polynomial equation larger than the 5th-degree. Knowing how to factorize is essential in these situations.

Answer 3

From my experience, it's been trial and error. Factoring a quadratic polynomial is basically the easy way out, but it's not always possible (ie. when the factors are not whole numbers or are imaginary). You can always solve using the quadratic equation, but it takes a lot less time and calculation if you can guess what the factors are right away. Factoring is also very useful to manipulate polynomials into a different form, for example for things to cancel out. It'll come in handy later, even if it isn't now.

Answer 4

If you are having trouble figuring out what to do, just use the formula every time. There's nothing wrong with that.

Answer 5

a hahahaha "factorised"?
wow!
if its in the form x^2+Bx+C then just try finding what multiplies to give you C and adds to give you B.
if you can't think of anything...use the formula

Answer 6

You should be recognizing patterns and able to do the factoring pretty quick in your head, if not use the formula.