Let #h(x)=6x^55x^4+4x^33x^22x+x+7# and #m(x)=x^21#, how do you find the quotient h(x) and m(x)?
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To find the quotient of h(x) and m(x), you can use polynomial long division. Divide h(x) by m(x) by following these steps:

Arrange the polynomials in descending order of powers. h(x) = 6x^5  5x^4 + 4x^3  3x^2  2x + x + 7 m(x) = x^2  1

Divide the highest power term of h(x) by the highest power term of m(x). Divide 6x^5 by x^2, which gives 6x^3.

Multiply the divisor (x^2  1) by the quotient obtained in step 2 (6x^3). 6x^3 * (x^2  1) = 6x^5  6x^3

Subtract the result obtained in step 3 from h(x). (6x^5  5x^4 + 4x^3  3x^2  2x + x + 7)  (6x^5  6x^3) = 5x^4 + 10x^3  3x^2  2x + x + 7

Repeat steps 24 with the new polynomial obtained in step 4. Divide 5x^4 by x^2, which gives 5x^2. 5x^2 * (x^2  1) = 5x^4 + 5x^2
(5x^4 + 10x^3  3x^2  2x + x + 7)  (5x^4 + 5x^2) = 10x^3  8x^2  3x + x + 7

Repeat steps 24 with the new polynomial obtained in step 5. Divide 10x^3 by x^2, which gives 10x. 10x * (x^2  1) = 10x^3  10x
(10x^3  8x^2  3x + x + 7)  (10x^3  10x) = 8x^2 + 7x + 7

Repeat steps 24 with the new polynomial obtained in step 6. Divide 8x^2 by x^2, which gives 8. 8 * (x^2  1) = 8x^2 + 8
(8x^2 + 7x + 7)  (8x^2 + 8) = 7x  1

Repeat steps 24 with the new polynomial obtained in step 7. Divide 7x by x^2, which gives 0.
0 * (x^2  1) = 0
(7x  1)  0 = 7x  1

The final result is the quotient obtained from all the divisions: 6x^3  5x^2 + 10x  8 with a remainder of 7x  1.
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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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