# Shortcut for Factoring Polynomials

• Mar 20th 2011, 05:18 AM
dumluck
Shortcut for Factoring Polynomials
Hi,
Quick question.

Say we have a polynomial $\displaystyle k^2 + k - 12$, one can use FOIL to find the factors.

However, is there a shortcut for doing the opposite.

i.e. I have $\displaystyle (k-3)(k+4)$ but want to find the polynomial? What confused me is that $\displaystyle - 3.-4$ will give -12 but so will $\displaystyle +3.-4$.

Thanks
• Mar 20th 2011, 05:20 AM
janvdl
Quote:

Originally Posted by dumluck
Hi,
Quick question.

Say we have a polynomial $\displaystyle k^2 + k - 12$, one can use FOIL to find the factors.

However, is there a shortcut for doing the opposite.

i.e. I have $\displaystyle (k-3)(k+4)$ but want to find the polynomial? What confused me is that $\displaystyle - 3.-4$ will give -12 but so will $\displaystyle +3.-4$.

Thanks

A minus times a minus cannot give you a minus. It gives you a plus.

-3 x -4 = +12
• Mar 20th 2011, 05:46 AM
Plato
Quote:

Originally Posted by dumluck
Say we have a polynomial $\displaystyle k^2 + k - 12$, one can use FOIL to find the factors.
However, is there a shortcut for doing the opposite.
i.e. I have $\displaystyle (k-3)(k+4)$ but want to find the polynomial? What confused me is that $\displaystyle - 3.+4$ will give -12 but so will $\displaystyle +3.-4$

Look at the linear term, $\displaystyle \mathbf+k$. That $\displaystyle +$ tells us that it is $\displaystyle -3,~+4$. Do you see why?
• Mar 20th 2011, 05:54 AM
dumluck
Quote:

Originally Posted by Plato
Look at the linear term, $\displaystyle \mathbf+k$. That $\displaystyle +$ tells us that it is $\displaystyle -3,~+4$. Do you see why?

Thanks Plato. I don't see why I'm afraid. could +k not equally denote that is could be -4, +3? It would equate to -12?
• Mar 20th 2011, 06:01 AM
Plato
Quote:

Originally Posted by dumluck
Thanks Plato. I don't see why I'm afraid. could +k not equally denote that is could be -4, +3? It would equate to -12?

If you add $\displaystyle +3~\&~-4$ we get $\displaystyle -1$ not $\displaystyle +1k$. But $\displaystyle -3+4=+1k$.
• Mar 20th 2011, 06:07 AM
dumluck
Quote:

Originally Posted by Plato
If you add $\displaystyle +3~\&~-4$ we get $\displaystyle -1$ not $\displaystyle +1k$. But $\displaystyle -3+4=+1k$.

ah ok so $\displaystyle (k + (b))(k + (c))$ must translate to $\displaystyle (k)^2 + (b+c)k + (b.c)$?