Question

how do you factor: 4x^2-13x+3

Answer 1

I was factoring this buddy here and I got carried away and lost.

Answer 2

The final value of the expression is 3, so the only way you can really distribute the last values are 3 and 1.
The exponential value is 4, so you can only multiply either 2 and 2, or 4 and 1 together.
The middle value is the sum of the products. (If I don't make any sense here, the collaboration of these facts should give you an idea of what I'm getting at).

Since it is a (- +) pattern, the pairing of the factors MUST be negative. This is because two negatives multiply together to make a positive, and the sums of negatives can create a negative. No other pairing can create this pattern.

After much experimentation, the factorization should be
(4x - 1)(x - 3)
[The values I kinda spit out above match, do they not?]

Answer 3

So lets work this out together so I can understand clearly. Are you down?

Answer 4

\[4x ^{2}-13x+3\]

\[4(3) = 12\]

Numbers that multiply together give you 12 but added give you -13.

\[-1(-12) = 12 ........ -1 + -12 = -13\]

Now we have:

\[4x ^{2}-12x-x+13\]

When you factor that you get:

\[4x(x-3(-(x+13)\]

NOW IM STUCK. Lol.

Answer 5

Where do you go from that point on?

Answer 6

@magix430

Answer 7

The tactic for tackling this is known worldwide as FOIL, that is, First, Outside, Inside, Last.
When checking the factorization, you generally follow it as follows:
1) Multiply the first of both factors together:
4x * x = 4x^2
2) Multiply the first of the first factor, and the last of the second factor together:
4x * -3 = -12x
3) Multiply the last of the first factor, and the first of the second factor together:
x * -1 = -x
4) Multiply the lasts of both factors together:
-3 * -1 = (positive) 3

Finally, you add these values all together in one big equation:
\[4x ^{2} - 12x - x + 3\]
or
\[4x ^{2} - 13x +3\]

Answer 8

The entire process of accomplishing this stuff is no easy task and takes a lot of time. However, with lots of practice, you will be attacking these problems with ease. I wish you good luck!