Question

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?

Answer 1

Answer:

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