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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?

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  1. help_people
    • one year ago
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    @phi

  2. anonymous
    • one year ago
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    Well, 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)

  3. help_people
    • one year ago
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    ok so could we start with each part so may we first start with part a?

  4. anonymous
    • one year ago
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    Sure, for part a, expand the product (4x+5)(3x+10) and get the expression.

  5. help_people
    • one year ago
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    ok could you show me?

  6. anonymous
    • one year ago
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    Well, \((4x+5) (3x+10) = 12x^2 + 40x + 15x + 50\) (using distributive law of multiplication) So, collecting similar terms, the final expression is \(12x^2 + 55x +50\)

  7. anonymous
    • one year ago
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    So the area will be \((12x^2 + 55x +50)\) square units.

  8. help_people
    • one year ago
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    may you possibly show me the work it helps me better?

  9. anonymous
    • one year ago
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    Well, 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.

  10. help_people
    • one year ago
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    srry i left :( may you help with part b? now ?

  11. help_people
    • one year ago
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    @adxpoi

  12. anonymous
    • one year ago
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    Sure, so what's the degree of the polynomial expression we obtaine in part a?

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