Math homework help with polynomials- 3xSQUARED - 16xy+5ySQUARED?

Question

how do I do polynomials like these? (two after exponents mean squared i couldn't figure out how to make them smaller then the other values)

3x2 - 16xy+5y2
2x2-11xy+5y2
5c2-8cd-4d2
3c2 + 4cd-4d2

Answer 1

Look in your text book under "factoring polynomials"... or you could try this web site that explains this fairly thoroughly...

http://faculty.ed.umuc.edu/~swalsh/Math%20Articles/Factoring.html

Answer 2

OK, let's take the first one.
Look first at the signs. Since you have a minus and then a plus, you know both factors have to be (somethingX - somethingY), since the middle term is negative, and the last term is positive.

So you now have (?X - ?Y) (?X - ?Y).
The center term has 16, and the outside terms are 3 and 5. 3*5 is 15, so if you utilize both of these, and 1*1 for the other, 15+1 = 16.

So therefore we get (3X - Y)(X - 5Y). Multiplying this out to check gives us 3x^2 - XY - 15XY + 5Y^2, so we are correct.

Do the rest of them the same way.
Good luck!

Answer 3

i) 3 x^2 - 16xy + 5 y2
= 3x^2 - xy - 15 xy + 5y^2
= x(3x - y) - 5y(3x - y)
= (3x-y) (x-5y)

ii) 2 x^2 - 11xy + 5 y2
= 2 x^2 - 1xy - 15xy + 5 y2
= x(2x - y) - 5y(2x - y)
= (2x - y) (x - 5y)

iii) 5c^2 - 8cd - 4 d^2
= 5c^2 - 10cd + 2cd - 4 d^2
= 5c(c - 2d) +2d(c - 2d)
= (5c + 2d) (c - 2d)

iv) 3c^2 + 4cd -4d^2
= 3c^2 + 6cd - 2cd -4d^2
= 3c(c + 2d) - 2d(c + 2d)
= (3c-2d) (c+2d)

So you see the secret lies in splitting the middle portion into such a way that you can take common variables out and regroup them into equations of single variable.

Answer 4

What are you trying to do with these?

You can factor them to:
(3x-y)(x-5y)
(2x-y(x-5y)
(5c+2d)(c-2d)
(3c-2d)(c+2d)