Factoring A Quadratic Equation?

Question

For the LIFE of me I cant solve the tiniest little factoring problem!

3x^2 + 11x - 4

Answer 1

What I learned was to take a*c,which here is 3 x 4 (absolute value) = 12

then list all possible factors of that number i.e., 12, which are (1,12),(2,6),(3,4) and see which of them sparks an association with the middle term '11'. From here it looks like 12 and -1.( We're talking addition here..)

You then write the original out again, but with the mibble 'bx' term split thus:

3x^2 +12x - x -4...

then follow this :

3x(x +4) -1 (x +4)...

take the 3x - 1 part and bracket it as one linear factor (3x -1) ...you may have too stare red-eyed for a while to see where I got 3x-1 from... but anyway, do that, and then take the other ( repeated) linear factor of (x + 4) and put it next to 3x - 1 thus:

(3x - 1)(x + 4)

seems like a lot of work but its a procedure which is useful in training your beseiged brain in other more difficult areas. And this is the whole point...

Answer 2

(3x - 1)(x + 4)

You just needed to find numbers that when multiplied together would give you 3 and -4, and when cross-multiplied and added together would give you 11.

Answer 3

3x^2+12x-x-4

3x(x+4)-1(x+4)

(x+4)(3x-1)