Question

Consider D(r) = 48r^5 – 243r^3.Part A: Determine which of the following are not factors of D(r). Select all that apply.a. 3r^5b. 7r - 16c. 4r - 9d. 4r + 9e. 7r + 16

Answer 1

The first thing that you must see

is that 3, is a common factor of 48, and 243.

$D(r)=48r^5-243r^3=3\cdot(16r^5-81r^3)$

Then we factor by r³, and we get the following

$D(r)=3\cdot r^3(16r^2-81)$

If we apply the difference of squares we get

$D(r)=3r^3(4r-9)\cdot(4r+9)$

Then, the elements that are NOT factos are 3r⁵,7r-16 and 7r+16, so the answers would be a,b,e