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How do you long divide #(12x³-11x²-27x-9) / (4x+3)#?

Answer 1

Sadie Alexander

#(12x^3-11x^2-27x-9)/(4x+3)=3x^2-5x-3#

#(12x^3-11x^2-27x-9)/(4x+3)#

#=1/4*(12x^3-11x^2-27x-9)/(x+3/4)#

#=1/4*(12x^2(x+3/4)-20x^2-27x-9)/(x+3/4)#

#=1/4*(12x^2(x+3/4)-20x(x+3/4)-12x-9)/(x+3/4)#

#=1/4*(12x^2(x+3/4)-20x(x+3/4)-12(x+3/4))/(x+3/4)#

#=1/4(12x^2-20x-12)#

#=3x^2-5x-3#

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Answer 2

Benjamin Achtenberg

To long divide (12x³ - 11x² - 27x - 9) by (4x + 3), follow these steps:

Divide the first term of the dividend (12x³) by the first term of the divisor (4x). This gives you 3x².
Multiply the entire divisor by the result from step 1 (3x²), which gives you 12x³ + 9x².
Subtract this result from the original dividend, which gives you -20x² - 27x - 9.
Bring down the next term from the original dividend, which is -9.
Repeat the process by dividing the first term of the new dividend (-20x²) by the first term of the divisor (4x), which gives you -5x.
Multiply the entire divisor by -5x, giving you -20x² - 15x.
Subtract this result from the new dividend, giving you -12x - 9.
Since the degree of the remaining term (-12x) is less than the degree of the divisor, you have the remainder.

So, the result of the long division is 3x² - 5x - 3 with a remainder of -9/(4x + 3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.