The amount of paint needed to cover a wall is proportional to its area. The wall is rectangular and has an area of 4z2 + 2z square meters. Factor this polynomial to find possible expressions for the length and width of the wall. (Assume the factors are polynomials.)
To factor the polynomial 4z^2 + 2z, we can first factor out the common factor, which is 2z:
2z(2z + 1)
Now we have factored 4z^2 + 2z as the product of 2z and 2z + 1.
To find the possible expressions for the length and width of the wall, we can use the factored form. Since the area of the rectangular wall is equal to 4z^2 + 2z, we have the following possibilities:
Length = 2z + 1, Width = 2z
or
Length = 2z, Width = 2z + 1