Question

Note: This is NOT a question. This is a tutorial.

how to factor quadratic expressions? For example you are given \(x^2 + 3x - 4\).

See comment below to see how

Answer 1

The first step would be to break down the middle term into addends such that the first addend is a factor of the first term (in this case we are given \(x^2\) as the first term), and the secod addend must be a factor of the last term (in this case we are given \(-4\) as the last term). Now, let us think of addends of +3x. Since our first term is positive, and our last term is negative, then our addends must have one positive, and one negative. The first trial would be +x and -4x. So let's try it.

\(x^2 + 3x - 4 = x^2 - x + 4x - 4\)

from here, we can clearly see that \((x^2 - x)\) is factorable, and \((4x - 4)\) is too. So let's factor them

\(x(x - 1)\) is the factored form of \((x^2 -x)\)

\(4(x-1)\) is the factored form of \((4x - 4)\)

So combining these data, we have...

\(x(x - 1) + 4(x - 1)\)

Notice how both terms have (x - 1). Therefore, we can say that (x-1) can be factored. If we do that, we'll have..

\((x-1)(x+4)\)

This is now the factored form of \(x^2 + 3x - 4\)

Answer 2

Why'd you ask haha?

Answer 3

because im bored...im doing tutorials :D

Answer 4

Good idea :)

Answer 5

lol my first paragraph had something wrong. "...The first trial would be +x and -4x" it should be -x and +4x. Please note this correction

Answer 6

There is an easier way..
\[a+b=-3\]
\[ab=-4\]
\[a = -4; b=1\]
so.. \[(x-4)(x+1)\]

Answer 7

(x+a)(x+b) = x^2 + x(a+b) + ab so you want 2 numbers...etc
Need to explain what if coefficient of x^2 is not 1
(Assuming "easy" factors)

Answer 8

i am not aware of this @Mimi_x3 o.O is that a real theorem? i mean is it ripped off from a real one (like binomial theorem or something)

Answer 9

lol, i can't remember what it is called..I tend to do it in my head.

How can it be the Binomial Theorem? lol

Answer 10

\[\LARGE x^{2} + 3x - 4\]
\[\LARGE x^{2} -x + 4x - 4\]
\[\LARGE x(x - 1) + 4(x - 1) \]
\[\LARGE (x + 4)(x - 1) \]
\[\LARGE \text {EASY, BABY ;)} \]

Answer 11

lol i do not know Mimi :p but at least i learned a new one today :) this discussion was a good idea after all

good work @ParthKohli :D

Answer 12

Want a Binomial Theorem example?

Answer 13

NO!

Answer 14

Its fun!!

Answer 15

@estudier 's algebraic equation is equivalent to the one you said mimi?

Answer 16

yeah right fun you sadistic bunny :P

Answer 17

c'mon you will love it :P

Answer 18

@lgbasallote Please edit the question. It's how to factor quadratic expressions, not equations. :)

Answer 19

thankk you for the correction :) and @Mimi_x3 i'll take permutation combination and probability but binomial theorem..NO WAY!

Answer 20

That's how I did it