How do you find the quotient of #(6x^3+5x^2+9)div(2x+3)# using long division?
Quotient:
(see below for derivation using long division)
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To find the quotient of (6x^3+5x^2+9) divided by (2x+3) using long division, follow these steps:
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Divide the first term of the dividend (6x^3) by the first term of the divisor (2x). The result is 3x^2.
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Multiply the entire divisor (2x+3) by the quotient obtained in step 1 (3x^2). The result is 6x^3+9x^2.
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Subtract the product obtained in step 2 (6x^3+9x^2) from the dividend (6x^3+5x^2+9). This gives you -4x^2+9.
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Bring down the next term from the dividend, which is 0x (since there is no x term).
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Divide the new dividend (-4x^2+9) by the first term of the divisor (2x). The result is -2x.
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Multiply the entire divisor (2x+3) by the quotient obtained in step 5 (-2x). The result is -4x^2-6x.
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Subtract the product obtained in step 6 (-4x^2-6x) from the new dividend (-4x^2+9). This gives you 15x+9.
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Bring down the next term from the dividend, which is 0.
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Divide the new dividend (15x+9) by the first term of the divisor (2x). The result is 7.5.
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Multiply the entire divisor (2x+3) by the quotient obtained in step 9 (7.5). The result is 15x+22.5.
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Subtract the product obtained in step 10 (15x+22.5) from the new dividend (15x+9). This gives you -13.5.
The final quotient is 3x^2 - 2x + 7.5, with a remainder of -13.5.
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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.
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.
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.
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.

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