Question

Please help will get a new fan and medal. Factor the following four-term polynomial.
2x+10+xy+5y

Answer 1

http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=15b128aa42d812ef9f3a9640bf1fb3fa&title=Factoring+Polynomials+Calculator&theme=gray&i0=x%5E4+-4x%5E3+%2B8x&podSelect&includepodid=Plot&showAssumptions=1&showWarnings=1 use this link to find it

Answer 2

i still do not understand

Answer 3

•Factor xy – 5y – 2x + 10.

Is there anything that factors out of all four terms? No. When you have four terms, and nothing factors out of all of them, think of factoring "in pairs". To factor "in pairs", I split the expression into two pairs of terms, and then factor the pairs separately.

xy – 5y – 2x + 10

What can I factor out of the first pair? I can take out a "y":

xy – 5y – 2x + 10

= y(x – 5) – 2x + 10

What can I factor out of the second pair? I can take out a "–2":

xy – 5y – 2x + 10

= y(x – 5) – 2x + 10

= y(x – 5) – 2(x – 5)

(I took out a –2, rather than a 2, because the leading sign on the pair was a "minus". And I got a "–5" in the result because, when I divided the positive10 by the negative2, the result was a negative5. Be careful with your signs!)

Now that I do have a common factor, I can proceed as usual:

xy – 5y – 2x + 10

= y(x – 5) – 2(x – 5)

= (x – 5)(y – 2)





ADVERTISEMENT







Factoring "in pairs" is most commonly used to introduce factoring quadratics. So you may see exercises that look like this:
•Factor x2 + 4x – x – 4.

This polynomial has four terms with no factor common to all four, so I'll try to factor "in pairs":

x2 + 4x – x – 4

= x(x + 4) – 1(x + 4)

= (x + 4)(x – 1)

In the second line above, I factored a "1" out. Why? If "nothing" factors out, a "1" factors out.
•Factor x2 – 4x + 6x – 24.

I'll try to factor "in pairs": Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

x2 – 4x + 6x – 24

= x(x – 4) + 6(x – 4)

= (x – 4)(x + 6)