A Bit O' Trouble Here...

[Haicee]

Even though my class has not gone over factoring using the distributive property yet, I've decided to learn ahead of time. What stumped me was this:

18x^2-30x-3x+5

I grouped up the factors and got the GCF for both of them, and got

6x(3*x-5)-1(3*x+5)

And the final answer I got was

(6x-1)(3x+5)

Now that just looks wrong, and I know that the real answer is (6x-1)(3x-5). Bu I just can't seem to get to that answer. Can anybody help?

 

[lookagain]

Even though my class has not gone over factoring using the distributive property yet,
I've decided to learn ahead of time. What stumped me was this:

18x^2-30x-3x+5

I grouped up the factors and got the GCF for both of them, and got

6x(3*x-5)-1(3*x+5) <---

And the final answer I got was

(6x-1)(3x+5)

Now that just looks wrong, and I know that the real answer is (6x-1)(3x-5). Bu I just can't seem to get to that answer. Can anybody help?

Halcee,

here is something else to know.

When you get 6x(3x - 5) from the first pair of terms of the expression to be factored,
for the expression to correctly factor, there must be a (3x - 5) factor to come out of
the second pair of terms to be factored.

Deliberately write down this factor to the right of 6x(3x + 5) and leave a couple of spaces for
an addition or subtraction sign and a factor to multiply by (3x - 5):


\(\displaystyle 6x(3x - 5) \ \ \ ?(3x - 5)\)


Look at the question mark. Ask what has to be multiplied by 3x to get the third term, -3x.

Here the common factor is the constant -1. But write it in as


6x(3x - 5) - 1(3x - 5)


Then, check to make sure that (-1)(-5) = 5, the 5 being the last term of the expression to be factored.

That checks, so you know that 18x^2 - 30x - 3x + 5 = 6x(3x - 5) - 1(3x - 5) is one of the correct
steps on the way to completely factoring this polynomial.





---> Just leave out the asterisks for multiplication. "3x" is sufficient.



(I do these steps quickly mentally, and it helps me to not get confused about whether
I will be factoring out a positive sign or a negative sign from the second pair of
terms of the expression to be factored.