How do you divide #(6x^4+12x+4)/(3x^2+2x+5)#?
Taken you to a point where you can continue from. Method is demonstrated.
This should be sufficient to illustrate the process. At this point, I'll hand things over to you.
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To divide (6x^4+12x+4) by (3x^2+2x+5), you can use long division or synthetic division. Here is the stepbystep process using long division:

Divide the highest degree term of the numerator (6x^4) by the highest degree term of the denominator (3x^2). The result is 2x^2.

Multiply the entire denominator (3x^2+2x+5) by the result from step 1 (2x^2). This gives you 6x^4+4x^3+10x^2.

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

Bring down the next term from the numerator (12x). The new expression becomes 4x^3+2x^2+12x+412x.

Divide the highest degree term of the new expression (4x^3) by the highest degree term of the denominator (3x^2). The result is (4/3)x.

Multiply the entire denominator (3x^2+2x+5) by the result from step 5 ((4/3)x). This gives you (4/3)x^3+(8/3)x^2+(20/3)x.

Subtract the result from step 6 from the new expression (4x^3+2x^2+12x+412x). This gives you (4/3)x^3+(2/3)x^2(8/3)x+4.

Bring down the next term from the numerator (8). The new expression becomes (4/3)x^3+(2/3)x^2(8/3)x+4+8.

Divide the highest degree term of the new expression ((4/3)x^3) by the highest degree term of the denominator (3x^2). The result is (4/9)x.

Multiply the entire denominator (3x^2+2x+5) by the result from step 9 ((4/9)x). This gives you (4/9)x^3+(8/9)x^2+(20/9)x.

Subtract the result from step 10 from the new expression ((4/3)x^3+(2/3)x^2(8/3)x+4+8). This gives you (4/9)x^3+(2/9)x^2(28/9)x+12.
The final result of the division is (2x^2+(4/3)x+(4/9)) with a remainder of (12).
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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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