Question

Remember that perimeter means distance around. Write the perimeter of the rectangle to the

right as a simplified polynomial. Then factor the polynomial.
Write the perimeter of the rectangle as a simplified polynomial.
The simplified polynomial for the perimeter is.
(Do not factor.)
x² + 3x
6x + 18
Q

Answer 1

The perimeter of the rectangle expressed as a simplified polynomial is P = 2x² + 18x + 36. After factoring out the common term, we get P = 2(x² + 9x + 18).

Step-by-step explanation:

To write the perimeter of a rectangle as a simplified polynomial, we add the lengths of all four sides. The lengths of the opposite sides of a rectangle are equal, so if one pair of sides is given by the polynomial x² + 3x and the other pair is given by 6x + 18, the perimeter (P) of the rectangle is:

P = 2 × (x² + 3x) + 2 × (6x + 18)

We now distribute the 2 into each term:

P = 2x² + 6x + 12x + 36

Next, we combine like terms:

P = 2x² + 18x + 36

This is the simplified polynomial for the perimeter of the rectangle. To factor the polynomial, we look for common factors in each term:

P = 2(x² + 9x + 18)

We can then try to factor the quadratic expression further, but in this case, the expression inside the parenthesis does not factor nicely, so we leave it as is.