Question

The rectangle below has an area of 15k^4 + 35k^3 + 20k^2. The width of the rectangle is equal to the greatest common monomial factor of 15k^4, 35k^3, and 20k^2. What is the length and width of the rectangle?

Answer 1

The greatest common factor is the biggest number that divides evenly into each one of the numbers without a remainder...the only thing that's different about our situation is that we have variables in addition to regular number (but the same logic applies...we need to find the biggest variable that goes into k^4 , k^3 , and k^2 ).

The biggest number that goes into 15, 35 and 20 is the number 5. The biggest variable that goes into k^4 , k^3 , and k^2 is k^2

Combining the number and the variable, we get that the greatest common monomial factor is 5k^2

Since area is length x width, and we just figured out that width is 5k2 , all we have to do to find length is divide 15k4+35k3+20k2 by 5k2 , and we get that the length is 3k^2+7k+4

So the width is 5k^2 and the length is 3k2+7k+4

:))

-Eli