How do you divide #(2x^3 - 2x^2 -5x + 6)/(x-2)#?
Expressing the numerator as factors of the divisor (x-2) is one method.
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To divide (2x^3 - 2x^2 - 5x + 6) by (x - 2), you can use long division or synthetic division. Here is the solution using long division:
2x^2 + 2x - 1
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x - 2 | 2x^3 - 2x^2 - 5x + 6 - (2x^3 - 4x^2) _______________ 2x^2 - 5x - (2x^2 - 4x) _______________ -x + 6 - (-x + 2) _______________ 4
Therefore, the quotient is 2x^2 + 2x - 1 and the remainder is 4.
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To divide the polynomial (2x^3 - 2x^2 - 5x + 6) by (x - 2), you can use long division or synthetic division. I'll demonstrate the process using long division:
Step 1: Divide the first term of the dividend (2x^3) by the divisor (x - 2), which gives (2x^2). Step 2: Multiply (2x^2) by (x - 2) to get (2x^3 - 4x^2). Step 3: Subtract (2x^3 - 4x^2) from the original dividend to get (-2x^2 - 5x + 6). Step 4: Bring down the next term, which is (-5x). Step 5: Repeat the process by dividing the first term of the new dividend (-2x^2) by (x - 2), which gives (-2x). Step 6: Multiply (-2x) by (x - 2) to get (-2x^2 + 4x). Step 7: Subtract (-2x^2 + 4x) from the current dividend to get (-9x + 6). Step 8: Bring down the next term, which is (6). Step 9: Repeat the process by dividing the first term of the new dividend (-9x) by (x - 2), which gives (-9). Step 10: Multiply (-9) by (x - 2) to get (-9x + 18). Step 11: Subtract (-9x + 18) from the current dividend to get (0).
Therefore, the quotient is (2x^2 - 2x - 9) with no remainder.
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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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