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help_people
 one year ago
A rectangle has sides measuring (4x + 5) units and (3x + 10) units.
Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for polynomials?
help_people
 one year ago
A rectangle has sides measuring (4x + 5) units and (3x + 10) units. Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. Part B: What are the degree and classification of the expression obtained in Part A? Part C: How does Part A demonstrate the closure property for polynomials?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, the area of a rectangle is simply the product of the two sides, in this case, (4x+5)(3x+10) sq.units. Expand the product to get the actual expression. It will be a degree 2 polynomial. Assuming, we are talking about the ring of polynomials with real coefficients, see that the product is also a polynomial with real coefficients so we have closure under multiplication ( can say the same if we are talking about the ring of polynomials with integer or rational coefficients)

help_people
 one year ago
Best ResponseYou've already chosen the best response.0ok so could we start with each part so may we first start with part a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sure, for part a, expand the product (4x+5)(3x+10) and get the expression.

help_people
 one year ago
Best ResponseYou've already chosen the best response.0ok could you show me?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, \((4x+5) (3x+10) = 12x^2 + 40x + 15x + 50\) (using distributive law of multiplication) So, collecting similar terms, the final expression is \(12x^2 + 55x +50\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the area will be \((12x^2 + 55x +50)\) square units.

help_people
 one year ago
Best ResponseYou've already chosen the best response.0may you possibly show me the work it helps me better?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, multiplying the two expressions goes like this: (4x+5)(3x+10) = 4x*(3x+10) + 5*(3x + 10) = 4x*3x + 4x*10 + 5*3x + 5*10 = \(12x^2 + 40x + 15x + 50 \) = \( 12x^2 + 55x + 50\) Hope, that clears it.

help_people
 one year ago
Best ResponseYou've already chosen the best response.0srry i left :( may you help with part b? now ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sure, so what's the degree of the polynomial expression we obtaine in part a?
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