How do you divide #(x^4-2x^3-2x^2+9x+3)/(x^2-3) #?

Answer 1

#(x^4-2x^3-2x^2+9x+3)/(x^2-3) = (x^2-2x+1) + (3x+6)/(x^2-3)#

I like to long divide the coefficients, not forgetting to include #0#'s for any missing powers of #x#. In our example, that means the missing #x# term in the divisor, which is therefore repesented as #1, 0, -3#.

The process is similar to long division of numbers.

We find a quotient #1, -2, 1#, meaning #x^2-2x+1# and remainder #3, 6#, meaning #3x+6#

So: #(x^4-2x^3-2x^2+9x+3)/(x^2-3) = (x^2-2x+1) + (3x+6)/(x^2-3)#

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Answer 2

To divide (x^4-2x^3-2x^2+9x+3) by (x^2-3), you can use long division.

First, divide the highest degree term of the numerator (x^4) by the highest degree term of the denominator (x^2). This gives x^2.

Multiply x^2 by the denominator (x^2-3), which gives x^4-3x^2.

Subtract this result from the numerator (x^4-2x^3-2x^2+9x+3) to get (-2x^3+7x^2+9x+3).

Next, repeat the process by dividing the highest degree term of the new numerator (-2x^3) by the highest degree term of the denominator (x^2). This gives -2x.

Multiply -2x by the denominator (x^2-3), which gives -2x^3+6x.

Subtract this result from the new numerator (-2x^3+7x^2+9x+3) to get (x^2+3x+3).

Now, divide the highest degree term of the new numerator (x^2) by the highest degree term of the denominator (x^2). This gives 1.

Multiply 1 by the denominator (x^2-3), which gives x^2-3.

Subtract this result from the new numerator (x^2+3x+3) to get (3x+6).

Since the degree of the new numerator (3x+6) is less than the degree of the denominator (x^2-3), the division is complete.

Therefore, the quotient is x^2-2x+1 and the remainder is (3x+6).

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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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