More Factoring

Last Thursday we went over the homework and everyone got up and did a problem, from the homework, on the board. After this Mr. Cople gave us a worksheet with some factoring problems and we spent all of class working on the worksheet. The homework was assignment 1103B.

Here are some of the problems from the worksheet:
(they are numbered according to their number on the worksheet)

14. x^2+6x-16

in order to do this problem we first have to list out all the multiples of 16 and find which set adds to 6 and multiplies to -16.

2 and 8: no
1 and 16: no
4 and 4: no
-2 and 8: yes

-2 and 8 add to 6 and multiply to -16.
Now we have to place our parentheses with an x in each one because we have to split up the x^2 into two separate x's.
So it will look like this: (x )(x ).
Next we plug in our -2 and 8 in any order.
So the final answer is: (x-2)(x+8) or (x+8)(x-2).


27. t^4-16

In order to do this problem we first have to find out what numbers will multiply to -16.

4 and 4: no
2 and 8: no
1 and 16: no
-4 and 4: yes

Now we can place our parentheses with our t's in them. However these ones will be t^2 because we started with a t^4.
So it will look like this: (t^2 )(t^2 ).
Now we plug in the -4 and 4.
So it will look like this: (t^2-4)(t^2+4).
But we are not done yet. We have to split up one of the equations in one of the parentheses.
So the final result will be: (t+2)(t-2)(t^2+4)
This works because 2*-2*4=-16.


22. a^2-12a+36

In order to do this problem we have to find multiples of 36 that add up to -12.

4 and 9: no
3 and 12: no
1 and 36: no
6 and 6: no
-6 and -6: yes

This works because -6 and -6 add to -12 and they multiply to 36.
Now we can place our parentheses with our a's in them.
So it will look like (a )(a ).
Now we can plug in -6 and -6.
So it will look like (a-6)(a-6).
Since -6 is in both pairs of parentheses we can combine them.
So the final answer is (a-6)^2.

I hope this was helpful and 1103B is due on April 29, 2011 because of PSAE practice on Monday and Tuesday and no school on Wednesday and very short classes on Thursday.


Owen C.