more math help me please?

Question

the problem was this

one factor of 3a^2 - 13a - 10 is

how do you do this how do you factor this please help me!!

Answer 1

You just have to look a little at the numbers.

(3a + 2)(a - 5) = 3a^2 - 13a - 10

In an equation like this Ma^2 + Pa + N you must look at the numbers M and N and their factors. You start with integer values but you might have to use fractions.
M is 3 and 1...... call the two you use m1 and m2
N is -10 and 1 or -5 and 2 or 10 and -1 or 5 and -2 ... n1 and n2

Finding the combinations of m1/m2 and n1/n2 is just finding factors of numbers like 12 or 27. The harder one is finding the combination of these that gives the value for P.

So your factoring looks like: (m1x + n1)(m2x + n2)
m1*m2 = M
n1*n2 = N
m1*n2 + m2*n1 = P

And then find the combinations that give the right value for P.
m1*n2 + m2*n1 = 3*(-10) + 1*1 = -28 .... Nope
m1*n2 + m2*n1 = 3*(-5) + 1*2 = - 13 .... And this looks good

I might have tried too hard to make it general but I hope it helps

Answer 2

There is a rule that says : pull a number out of the air. Plug it into the expression. If the expression works out to zero, then a- that number is a factor.
It is usual to start off with low numbers. I'll pick 1.
3a^2-13a-10 becomes
3(1)^2-13(1) -10 works out to -20. Not good. I'll try -1. I get 3(-1)^2 -13(-1) -10 works out to 3+13 -10. Not good. You keep on doing this until you try 5.
3(5)^2-13(5) -10=0 Yes! 75-65-10
That means a-5 is a factor.
Now since this is an equation that contains the power 2 and no higher(as in 3a^2), it will have two, and only two factors. They will look like this:
(?.........?)(?........?)
We know a-5 is a factor so we can fill in one factor,
(a-5)(?.......?)
We know the other factor must have 3a, in order to give us 3a^2, so we now have (a - 5)(3a.....?)
We need to get 10, so the number we need to go with5 is 2. (a-5)(3a...2). What sign?. It has to yield -10, so it must be +2
(a - 5)(3a + 2).
That's one way to do it. I've taken this explanation a bit farther than was called for. After all, we were asked to find one factor, and we did that early on. Just thought you might like to see the second factor.
There are other ways to factor, but we'll leave that for another time. Good luck!

Answer 3

you could draw a pic to help i got (3a+2)(a-5)