How do you divide #(2x^3 - 2x^2 -5x + 6)/(x-2)#?

Answer 1

#2x^2+2x-1+4/(x-2)#

Expressing the numerator as factors of the divisor (x-2) is one method.

#color(red)(2x^2)(x-2)+(color(blue)(+4x^2)-2x^2)-5x+6#
#=color(red)(2x^2)(x-2)color(red)(+2x)(x-2)+(color(blue)(+4x)-5x)+6#
#=color(red)(2x^2)(x-2)color(red)(+2x)(x-2)color(red)(-1)(x-2)+(color(blue)(-2)+6)#
#rArr(2x^3-2x^2-5x+6)/(x-2)#
#=color(red)(2x^2+2x-1)+4/(x-2)#
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Answer 2

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
___________________

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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Answer 3

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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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.

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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