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Answer :
4x^2-36/x+3
4(x^2-9)/x+3
4(x-3)(x+3)/x+3
4(x-3) or 4x-12
4(x^2-9)/x+3
4(x-3)(x+3)/x+3
4(x-3) or 4x-12
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Final answer:
The quotient of 4x² - 36 divided by x + 3 is 4(x - 3), obtained by factoring and cancelling out the common terms.
Explanation:
The quotient when 4x2 - 36 is divided by x + 3 is found using polynomial long division or synthetic division. To start, recognize that 4x2 - 36 can be factored as 4(x2 - 9), which is a difference of squares and further factors into 4(x + 3)(x - 3). When you divide this expression by x + 3, the x + 3 terms cancel out, leaving you with a quotient of 4(x - 3).
Therefore, as per the above explaination, the required quotient is 4(x - 3).
