Beth is painting a picture. She usually buys acrylic paints at Michaels for $5.25 a tube. She runs out of black paint so she goe
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Answer:
- 5yz^2 - 3z^2 - 5y + 7
Step-by-step explanation:
The polynomial is:
( 1 )
this polynomial is the result of the sum of two polynomials, one of them given by
( 2 )
if you find to know what is the other polynomial, you can take the difference between the polynomial (1) and (2). It is necessary to take the difference between simmilar terms, as follow:
- yz^2 - 3z^2 - 4y + 4
<u>- (4yz^2 + y - 3 )</u>
<u />
- yz^2 - 3z^2 - 4y + 4
<u> - 4yz^2 - y + 3 </u>
- 5yz^2 - 3z^2 - 5y + 7
hence the other polynomial is - 5yz^2 - 3z^2 - 5y + 7
This is not an identity but an equation. You're supposed to find the values of for which this is true. It is *not* true for all values of
.
To see why:
has period
, which means
.
The angle sum identity for says that
So
By definition of ,
and so
which is only 0 if either (which only happens for certain values of
) or
(which also only happens for certain values of
). It's these values of
you want to find.
whenever
is a multiple of
, i.e.
for any integer
.
If , then
is true for
and
. Then to account for all other possible values, we add a multiple of
, so that
or
for integers
.