Question

10x^2-46xy-20y^2

Answer 1

Where did you get this question from?

Answer 2

my homework the teacher is asking us to do this and im lost

Answer 3

I guess it really doesn't matter. For many of these quadratics, you have to first factor out a number that is common to all three terms before starting the quadratic factorization.

Answer 4

If you notice that the coefficients of each term is divisible by the same number, you can factor that number out first. Then, afterwards, you can begin the quadratic factorization.

Answer 5

In this case, the coefficient in each term is divisible by 2, therefore factor 2 out of each:

2(5x^2 - 23xy - 10y^2)

Answer 6

Now we can factor this the way we usually do.

Answer 7

Find 2 numbers that multiply to get -50, but add to get -23:

mn = (5)(-10)
m + n = -23

Answer 8

2 and -25

Answer 9

Very good. Now, you still do the same thing you normally would, but we will just keep the 2 out in front because it is still part of the factorization.

So 2(5x^2 - 23xy - 10y^2) will become:

2(5x^2 - 25xy + 2xy - 10y^2)

Notice that -23xy = -25xy + 2xy

Answer 10

Now you factor the first two terms inside the parentheses. Then factor the last two terms in the parentheses. Afterwards, you should notice a binomial that is common to both. After you factor out that binomial, you will be done.

Answer 11

5x is common to the first two terms, 2y is common to the last two terms so:

2(5x(x - 5y) + 2y(x - 5y))

x - 5y is the common binomial, so factoring that out results in this:

2((x - 5y)(5x + 2y))

Lastly, multiply the two back in to the first set of parentheses to present the factorization as a product of three factors:

2(x - 5y)(5x + 2y)

Answer 12

In order to get comfortable with doing these kinds of factorizations, you have to get comfortable with doing the easier ones.

Answer 13

ok i have been working on the easier ones and i think im geting good

Answer 14

i hope any ways

Answer 15

Did you at least understand the steps above?

Answer 16

yes i did

Answer 17

Well, that's great. Good luck on your test.

Answer 18

thank you