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Create a real-life application math problem that involves multiplying one or more polynomials.

a) Solve the equation 2x^2 + 3x - 5 = 0
b) Multiply (x + 2)(x - 3)
c) Find the area of a rectangular garden with sides (2x + 1) and (3x - 2)
d) Factor the expression 4x^2 - 9

1 Answer

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Final answer:

The solution involves solving a quadratic equation using the quadratic formula, multiplying binomials, finding the area of a rectangle expressed with polynomials, and factoring a difference of squares.

Step-by-step explanation:

Real-life application problems that involve multiplying polynomials are common in various fields such as engineering, economics, and physical sciences. Here are the solutions to the parts of the question:

  1. Solving the equation 2x^2 + 3x - 5 = 0 can be done using the quadratic formula. This is a mathematical function known as a second-order polynomial or quadratic function:
  2. Multiplying binomials like (x + 2)(x - 3) involves applying the distributive property, also known as the FOIL method in this case.
  3. To find the area of a rectangular garden with sides represented by the polynomials (2x + 1) and (3x - 2), you multiply the two expressions, which is another example of polynomial multiplication.
  4. Factoring the expression 4x^2 - 9 involves recognizing it as a difference of squares and applying the appropriate factoring technique.

Now, let's solve each part in detail:

  1. Solve the quadratic equation 2x^2 + 3x - 5 = 0 using the quadratic formula:
    x =
    [-b ± √(b^2 - 4ac)] / (2a)

    Here, a = 2, b = 3, and c = -5. Plug these values into the formula to find the values of x.

  2. Multiply (x + 2)(x - 3) by expanding the expression:
    (x + 2)(x - 3) = x^2 - 3x + 2x - 6

    Simplify it to:
    x^2 - x - 6

  3. For the rectangular garden, multiply (2x + 1) by (3x - 2) to get the area:
    A = (2x + 1)(3x - 2)

    Expand it to:
    A = 6x^2 - 4x + 3x - 2

    Simplify it to:
    A = 6x^2 - x - 2

  4. Factor the expression 4x^2 - 9 by recognizing the pattern a^2 - b^2 = (a + b)(a - b):
    4x^2 - 9 = (2x)^2 - (3)^2

    Factor it into:
    (2x + 3)(2x - 3)

User AlekseyS
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