Question

The amount of paint needed to cover a wall is proportional to its area. The wall is rectangular and has an area of 6z^2 + 6z square meters. Factor this polynomial to find possible expressions for the length and width of the wall. (Assume the factors are polynomials.)

Answer 1

We can factor the polynomial 6z² + 6z as follows:

`6z^2 + 6z = 6z(z + 1)`

We can use this factorization to express the area of the wall as the product of two factors:

`6z^2 + 6z = 6z(z + 1) = length × width`

Therefore, the length of the wall is 6z, and the width of the wall is z + 1.