We were recently given a worksheet with some problems on it and I'm struggling with a few of the problems. Can anyone lead me in the direction or show me how to do some of these factoring problems?
Factor Fully.
1) 28s^2 - 8st - 20t^2
2) y^2 - (r - n)^2
3) 10x^2 + 38x + 20
4) y^5 - y^4 + y^3 - y^2 + y - 1
I'd greatly appreciate any help given for any of these problems. Thank you!
First rule, factor any constant out of the whole thing that you can:
Now, since 7 and 5 are prime all we need to do is arrange the 7 and 5 in some way to multiply out correctly. Trial and error gives me:
Remember ?
Let a = y, b = r - n.
This can't be factored any further than this.
This is a fun one, isn't it? Factor by grouping:
Notice that both terms in parenthesis are the same, so we can factor again:
Now, the second factor can't be factored any further, but the first term can:
So
-Dan
Thanks so much for all the help! That all made perfect sense.
I have a few more questions that I am struggling with if you'd be so kind as to direct me in the correct path:
1) 3v^2 - 11v - 10
Personally I don't think this one can be factored, as nothing multiplies to (-30) and adds to (-11).
2) h^3 + h^2 + h + 1
3) 9(x + 2y + z)^2 - 16(x - 2y + z)^2
All help will be greatly appreciated.
Here's where I'm stuck for the 2nd one:
h^3 + h^2 + h + 1
= h(h^2 + h + 1) + 1
Now I need two numbers that multiply to 1, but also add to 1 - which doesn't make sense to me. =/
EDIT AGAIN:
Solved this one!
Anyone have any ideas about the other two?