Describe how to find linear expressions for the possible dimensions of a rectangular prism with a volume of 8k(cubed) + 26K(squared) +6K.
Sigh... this is what the 21st century has come to.........
8k^3 + 26k^2 + 6k.
2k(4k^2+13k+3)
2k(x+1/4)(x+3).
Describe how to find linear expression for the possible demension of a rectangular prism with the volume of 8k³+26k+6k
Who the hell cares anymore
To find the linear expressions for the possible dimensions of a rectangular prism with a given volume, we need to factorize the volume expression.
The given volume expression is 8k^3 + 26k^2 + 6k.
Step 1: Look for common factors
In this case, there is no common factor among the terms.
Step 2: Group the terms
Since we want to find linear expressions, we need to express the volume expression as a product of linear factors. We will group the terms in a way that allows us to factorize.
8k^3 + 26k^2 + 6k can be rewritten as:
(k^2)(8k + 26) + 6k
Step 3: Factorize each grouping
Factorize the expression within each grouping.
The first grouping:
(k^2)(8k + 26) can be further factorized as:
k^2(2(4k + 13))
The second grouping:
6k is already in its simplest form.
Step 4: Combine the factors
Combine the factors from both groupings.
The linear expressions for the possible dimensions are:
k^2(2(4k + 13)) * 6k
Simplifying further, we get:
12k^3(4k + 13)
Therefore, the linear expressions for the possible dimensions of the rectangular prism with the given volume are 12k^3 and (4k + 13).