A rectangular garden has a length of (x + 7) meters and a width of (2x - 3) meters. Write a polynomial function, A(x), that represents the area of the garden. Then, determine the area of the garden if x = 5 meters.

A(x) = 2x^2 + 11x - 21; A(5) = 64 square meters

A construction company is designing a storage unit. The dimensions are given by the polynomials (x + 2), (x + 3), and (2x - 1). Write a polynomial V(x) that represents the volume of the storage unit. What is the leading coefficient and degree of V(x)?

V(x) = 2x^3 + 9x^2 + 7x - 6; Leading coefficient: 2; Degree: 3

C(x) = 3x^3 + 5x^2 + 1.5x + 5; Cubic polynomial

I can construct a polynomial function to model a real-world scenario and analyze its behavior using multiplication.

1
When multiplying monomials, you can use the commutative property to rearrange terms and then add the exponents of like bases: 4x * 5x = 20x².
2
To multiply a monomial by a polynomial, use the distributive property to multiply the monomial by each term inside the polynomial: 4x(2x² + 7x + 3) = 8x³ + 28x² + 12x.
3
When multiplying (2x - 1)(7x + 6), use distributive property to multiply each term in the first binomial by each term in the second, then combine like terms to simplify: 14x² + 12x - 7x - 6 = 14x² + 5x - 6.