Answer:
The coefficient of the 2nd term is - 26
Step-by-step explanation:
- <em>Standard form of polynomial means its terms are ordered from greatest exponent to smallest exponent </em>
- <em>The leading coefficient in polynomial is the coefficient of the first term in a polynomial in standard form</em>
∵ 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
