Factor the following trinomial:

10x^3 - 71x^2 + 126x

Question

Factor the following trinomial:

10x^3 - 71x^2 + 126x

anonymous · Answer

Factors are:
10: 5*2 & 10*1
126: 126*1, 9*14 & 18*7

mertsj · Answer

First factor out the common factor which is x

the_fizicx99 · Answer

Try to first factor it as much as possible to make it easier.

It doesn't have a coefficient gcf but it does have a variable gcf (they all have x's)

Always pick the lowest value, here it's x.

x(10x^2 - 71x + 126x)

Now multiply 10 * 126, it gives you 1260.

Now you find a pair that when multiplied gives you 1260 but adds up to -71. 

Hint: Use negative numbers

the_fizicx99 · Answer

Opps, 

x(10x^2 - 71x + 126) *

the_fizicx99 · Answer

Still need help?

anonymous · Answer

lolololol this guy actually "factored" the trinomial. dam that is too funny.

anonymous · Answer

Yes, I still need help.

anonymous · Answer

ok so yes you have to factor out the greatest common factor, so what is the greatest common factor in this equation?

anonymous · Answer

uhhh, x?

anonymous · Answer

yep :D so take x and divide it throughout the equation so you get: x($$10^2-71x+126)$$

anonymous · Answer

Then what?

anonymous · Answer

ok give me one sec.

the_fizicx99 · Answer

There's a shortcut, what number adds 1260 but adds up to -71?

anonymous · Answer

I have no idea. lol

whpalmer4 · Answer

Try starting with 1/2 of 71.  Call it 35.  35 + ??? = 71?  Does 35*??? = 1260?

the_fizicx99 · Answer

u-u k... 

-35 * -36 = 1260
-35 + (-36) = -35 - 36 = -71

10x^2 - 35x - 36x + 126

5x(2x - 7) -18(2x - 7)

x[(2x-7)(5x-18)]

For some reason I can't use LaTeX, I was going to show you why you move 2x - 7 and 5x - 18 to the other side and still keep them... :/

whpalmer4 · Answer

If not, move to the next number down and try again, until you find a pair that works.

the_fizicx99 · Answer

I prefer to make a list of values.

whpalmer4 · Answer

easy if you have factored it or can do so at sight, less convenient with bigger numbers like 1260.  I wouldn't expect anyone asking for help factoring to be able to pluck those numbers out of the air!

whpalmer4 · Answer

factors of 10 that add to -7, sure.  Factors of 1260 that add to -71?  Maybe 1 in 10 student who has asked me for help factoring would get that without some assistance...

whpalmer4 · Answer

even the factors of 10 that add to -7 is a challenge for quite a few!

anonymous · Answer

5&2

the_fizicx99 · Answer

Actually I use a much simple method, 1 + 2 + 6 + 0 = 9, 1260/9 = 140 and I can find the values much faster, or because 1260 ends with a 0, it's divisible by 5. Anything that ends in 0 or 5 its divisible by 5

anonymous · Answer

This stuff is never this difficult in class lol

the_fizicx99 · Answer

It's not really difficult, if you know mental math it make sit much easier!

the_fizicx99 · Answer

makes it*

anonymous · Answer

Ok so yep I got x$$(5x-18)(2x-7)$$ and it works just as @tHe_FiZiCx99 had

anonymous · Answer

math is never easy lol

the_fizicx99 · Answer

Just requires patience and dedication :) It's another language :D

anonymous · Answer

it's beyond another language lol

anonymous · Answer

very true! :D

the_fizicx99 · Answer

cx

the_fizicx99 · Answer

Rose you forgot to add the "x"

x[(2x-7)(5x-18)]

anonymous · Answer

i  tried it add it but the program let the x go above the equation… but it is there only hiding (it doesn't want to be in the spotlight) ;P

the_fizicx99 · Answer

it goes inside the $$\ $$ or $\ $

the_fizicx99 · Answer

Well that failed, $\ \[ ~and~ \]$ or $\ $\ ~and ~ $ $\color{red}{$} $

anonymous · Answer

lol, I need help with the next one, I think.

the_fizicx99 · Answer

\[\ * and \(\ U_U

the_fizicx99 · Answer

Sure ask it I guess