Answer :
The quotient of the division using the long division rule is 4x^2 - x + 3
Synthetic division of functions
Polynomial functions are functions that has a leading degree of 3 and above. Given the following parameters.
Dividend = 4x³+ 11x2 +9
Divisor = x + 3
Using the synthetic division to determine the quotient
4x^2 - x + 3
x+3 | 4x³+ 11x2 +9
4x³ + 12x²
__________________
-x² + 0x
-x² - 3x
___________________
3x+9
3x+9
___________________
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Hence the quotient of the division using the long division rule is 4x^2 - x + 3
Learn more on synthetic division here: https://brainly.com/question/18788426
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