We have been given a polynomial and we are asked to factor our polynomial by double grouping.

First of all we will group terms with common factors. We can see that
and 2x have a common factor x. Common factor of -3x and -6 is -3.


Now we will factor out Greatest Common Factor from each group.
After factoring out GCF from each group we got (x+2) as our common binomial. Now we will write our polynomial as a product of two binomials as:
Therefore, our polynomial as a product of two binomials will be
.
Denise is the fastest runner. 40 divided by 6 is 6.666 repeating 30 divided by 5 is 6 and 20 divided by 4 is 5 therefore denise is fastest
Answer:
Make use of the fact that as long as
and
:
.
.
.
Step-by-step explanation:
Assume that
and
.
Make use of the fact that
and
to rewrite the given expression as a combination of
and
.
.
Since
:
.
Substitute this equality into the expression:
.
By the Pythagorean identity,
. Rearrange this identity to obtain:
.
Substitute this equality into the expression:
.
Again, make use of the fact that
to obtain the desired result:
.
Answer:
The imaginary part is 0
Step-by-step explanation:
The number given is:

First, we can expand this power using the binomial theorem:

After that, we can apply De Moivre's theorem to expand each summand:
The final step is to find the common factor of i in the last expansion. Now:



The last part is to multiply these factors and extract the imaginary part. This computation gives:


(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)
A calculator simplifies the imaginary part Im(x⁶) to 0