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30 March, 05:02

The length, width, and height of a rectangular box are represented by 2x, 3x + 1, and 5x - 6, respectively. When the volume is expressed as a polynomial in standard form, what is the coefficient of the 2nd term?

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  1. 30 March, 06:52
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    The coefficient of the 2nd term is - 26

    Step-by-step explanation:

    Standard form of polynomial means its terms are ordered from greatest exponent to smallest exponent The leading coefficient in polynomial is the coefficient of the first term in a polynomial in standard form

    ∵ The length, width, and height of a rectangular box are

    represented by 2x, 3x + 1, and 5x - 6

    ∴ l = 2x, w = 3x + 1, h = 5x - 6

    The formula of the volume of a rectangular box is V = l * w * h

    ∵ V = 2x (3x + 1) (5x - 6)

    - multiply the two brackets at first

    ∵ (3x + 1) (5x - 6) = (3x) (5x) + (3x) (-6) + (1) (5x) + (1) (-6)

    ∴ (3x + 1) (5x - 6) = 15x² + (-18x) + 5x + (-6)

    - Add the like terms

    ∴ (3x + 1) (5x - 6) = 15x² + (-18x + 5x) + (-6)

    ∴ (3x + 1) (5x - 6) = 15x² + (-13x) + (-6)

    - Remember (-) (+) = (-)

    ∴ (3x + 1) (5x - 6) = 15x² - 13x - 6

    Substitute it in V

    ∴ V = 2x (15x² - 13x - 6)

    - Multiply each term in the bracket by 2x

    ∴ V = 2x (15x²) - 2x (13x) - 2x (6)

    ∴ V = 30x³ - 26x² - 12x ⇒ in standard form

    ∵ The second term in the polynomial is - 26x²

    ∴ Its coefficient is - 26

    ∴ The coefficient of the 2nd term is - 26
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