Question

The owner of a hotel is installing a patio around three sides of her pool as shown. a rectangle inside the rectangle with three sides. the outer side rectangle is named a patio and the inside rectangle is named a pool. length l equals 2 squares of p plus 4p minus 6, area square of p minus 3p plus 2, width 3p, area width 5. which statements are true about the expression representing the area of the patio?

Answer 1

The area expression for the patio, (2p^2 + 4p - 6) * 3p, expands to 6p^3 + 12p^2 - 18p, a cubic polynomial with four terms, including a constant term of -18.

The expression for the area of the patio is (2p^2 + 4p - 6) * 3p. When expanded, this expression becomes 6p^3 + 12p^2 - 18p.

The expression representing the area of the patio has a constant term.

True. The constant term in the expression is -18.

The expression representing the area of the patio is a trinomial.

False. The expression is not a trinomial; it is a polynomial with three terms.

The expression representing the area of the patio has four terms.

True. The expression indeed has four terms: 6p^3, 12p^2, -18p, and the constant term -18.

The expression representing the area of the patio is a polynomial.

True. A polynomial is an expression with one or more terms, and this expression fits that definition.

The expression representing the area of the patio is cubic.

True. The highest power of the variable is p^3, making it a cubic expression.

In summary, the expression representing the area of the patio is a cubic polynomial with four terms, including a constant term.