what is the secret to factoring equations?

Question

the problem is 2x squared -13x-45 please help...I have no idea!!!!

Answer 1

2x² - 13x - 45
Now the only possible factors for 2x² are 2x and x so this may be written:-
(2x-------).(x-------)
Now require two numbers that multiply to - 45 and give - 13x when inserted in the brackets
These numbers are 5 and 9:-
(2x + 5).(x - 9)
x term given by 5x - 18x = - 13x
- 45 given by 5 X - 9
Answer is (2x + 5).(x - 9)
P.S. an equation needs an equals sign or it is not an equation.

Answer 2

2x² - 13x - 45 will factorise into the shape (2x + a)(x + b)

where the a and b are factors of -45. There are a lot of them and from here it is trial and error

1 and - 45
3 and -15
5 and -9
9 and -5
15 and -3
45 and -1


All of them will produce 2x² and -45 so you only need to look at the x term.

(2x + 45)(x - 1) = 2x² + 43x -45
(2x + 15)(x - 3) = 2x² + 9x - 45
(2x + 9)(x - 5) = 2x² - x - 45
(2x + 5)(x - 9) = 2x² - 13x - 45 found it

but to contiue for completeness

(2x + 3)(x - 15) = 2x² - 27x - 45
(2x + 1)(x - 45) = 2x² - 89x - 45

If it had been none of these we would have to try them with the signs the other way round

(2x - 45)(x + 1) = 2x² - 43x -45
(2x - 15)(x + 3) = 2x² - 9x - 45
(2x - 9)(x + 5) = 2x² + x - 45
(2x - 5)(x + 9) = 2x² + 13x - 45
(2x - 3)(x + 15) = 2x² + 27x - 45
(2x - 1)(x + 45) = 2x² + 91x - 45

With practice this gets easier and also a very large number in one of the brackets will produce a large x term and this can usually be ignored or left till later

Answer 3

Practice is the key to factorising especially when you start doing cubic's.....

(2x + 5)(x - 9) = 2x^2 - 13x - 45

If equation = 0
x = -5/2 or x = 9

Answer 4

The techniques are described by other answers here, but the real secret is 'patience'. If you go slow and easy, and follow the steps one at a time it will happen.

It also helps if you love numbers, like I do.