Question

how do you factor 5x^2-5x-30

Answer 1

first you must simplify the whole equation by a common factor, can u see what it is?

Answer 2

then it will be much easier to factorize.

Answer 3

First factor out the 5

Answer 4

In the equation divide 5x^2, 5x and 30 by five to factor out five.

Answer 5

Then you would get the equation x^2-x-6. And you would need to factor it by finding two numbers that add up to -1, and has a sum of -6.

Answer 6

find the roots of the equation

Answer 7

@mivanov It's not an equation.

Answer 8

i meant for her to find the roots of the equation 5x^2-5x-30=0

Answer 9

But the problem said to factor the expresson. That's why she can't divide by 5. She has to factor out the 5

Answer 10

Yes she has to divide by 5, in order to factor.

Answer 11

Oh I think I see what you mean... so the equation would look like this 5(x^2-x-6)

Answer 12

Yes. And then factor the trinomial inside the parentheses

Answer 13

Yeah your right I forgot about putting the 5 outside the para(), but everything else you so the same way.

Answer 14

@maria74123 you mean add up to -1 and have a product of -6

\[5x^2-5x-30 = (5x + a)(x+b)\] for some values of a and b. We know that 5 is prime, so one of the products will have a 5x and the other an x.

\[(5x+a)(x+b) = 5x^2 + 5bx + ax + ab = 5x^2 + (5b+a)x + ab\]but we want that to have the same form as our original expression, so we can see that the following must be true:\\[5b+a = -5, ab = -30\]
If we look at the factors of 30, we have 2, 3, 5, 6, 10, 15 to work with. 5(2) - 15 = -5, and 2*(-15) = -30, so our factored expression is
\[(5x-15)(x+2) or 5(x-3)(x+2)\]

Answer 15

Not necessary to factor out the 5 to factor the polynomial, but it might make factoring easier.

Answer 16

It is necessary if you want to factor completely.

Answer 17

Any typically, instructors want things factored completely.

Answer 18

No, I wasn't clear - it isn't necessary to factor the 5 out before factoring the trinomial.

Answer 19

I agree that it needs to come out somewhere for full factoring, but it doesn't have to be first.

Answer 20

Yeah I always learned to factor out that way, because it is easier. But everyone does it differently.... and yes I said that wrong, I meant find the product of -6, not sum Oops lol

Answer 21

@whpalmer4 Maybe not necessary but it certainly makes life easier to take out the 5 first.

Answer 22

All this work, and this girl juicepop2i sn't even online anymore Haha people drive me nuts!

Answer 23

It does, but practice factoring things where the leading coefficient != 1 makes factoring them when you can't simplify it more familiar. Practice doing more difficult things makes them easier when they can't be avoided.