Question

A rectangle has a height of 4 and a width of x^(2)+3x+2. Express the area of the entire rectangle. Expression should be expanded.

Answer 1

Sure, to find the area of a rectangle, we can use the standard formula: Area = Width * Height.

Here in this problem, the height of the rectangle is given as 4 and the width is expressed as a polynomial function in terms of x, i.e., x^(2) + 3x + 2.

Let's find the area by multiplying the width by the height.

=> Area = Height * Width
=> Area = 4 * (x^(2) + 3x + 2)

Now let's distribute the multiplication:

=> Area = 4*x^(2) + 4*3x + 4*2
=> Area = 4*x^(2) + 12x + 8

So the area of the rectangle, when expanded, is expressed as 4*x^(2) + 12x + 8.