How do you divide #(6x^4+9x^32x^2+2x7)/(4x2) #?
Use either synthetic division or polynomial long division to get
synthetic division #{: (,,6,+9,2,+2,7), (+,,,color(white)("X")3,color(white)("X")6,color(white)("X")2,color(white)("X")2), (,,"","","","",""), (/ (4),"",6,12,4,4,color(red)((5))), (xx (2),"",color(blue)(3/2),color(blue)(3),color(blue)(1),color(blue)(1),) :}#
Polynomial long division #{: (,,color(blue)(3/2x^3),color(blue)(+3x^2),color(blue)(+x),color(blue)(+1),), (,,"","","","",""), (4x2,")",6x^4,+9x^3,2x^2,+2x,7), (,,6x^4,3x^3,,,), (,,"","",,,), (,,,12x^3,2x^2,,), (,,,12x^3,6x^2,,), (,,,"","",,), (,,,,4x^2,+2x,), (,,,,4x^2,2x,), (,,,,"","",), (,,,,,4x,7), (,,,,,4x,2), (,,,,,"",""), (,,,,,,color(red)(5)) :}#
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To divide (6x^4+9x^32x^2+2x7) by (4x2), you can use long division. Here are the steps:

Divide the first term of the numerator (6x^4) by the first term of the denominator (4x). The result is 1.5x^3.

Multiply the entire denominator (4x2) by the result from step 1 (1.5x^3). This gives you 6x^4  3x^3.

Subtract the result from step 2 (6x^4  3x^3) from the original numerator (6x^4+9x^32x^2+2x7). This gives you 12x^3  2x^2 + 2x  7.

Bring down the next term from the original numerator (2x^2). The new numerator becomes 12x^3  2x^2 + 2x  7.

Repeat steps 14 with the new numerator (12x^3  2x^2 + 2x  7) and the original denominator (4x2).

Continue this process until you have divided all terms of the numerator.
The final result of the division is 1.5x^3  0.5x^2 + 1.5x  3.5, with a remainder of 0.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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