How do you divide #(x^4 - 3x^2+4x - 5)/(x+4)#?
Synthetic division. Answer:
We can either use long division or synthetic division, but since we are dividing by a linear equation, synthetic division would be easier.
For synthetic division, we divide the coefficients of the dividend by the value of
Therefore, our answer is
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To divide (x^4 - 3x^2 + 4x - 5) by (x + 4), you can use long division or synthetic division. Here is the step-by-step process using long division:
- Divide the first term of the numerator (x^4) by the first term of the denominator (x). This gives x^3.
- Multiply the entire denominator (x + 4) by x^3, which gives x^4 + 4x^3.
- Subtract this result from the numerator (x^4 - 3x^2 + 4x - 5) to get -7x^3 - 3x^2 + 4x - 5.
- Bring down the next term from the numerator, which is -7x^3. Now you have -7x^3 - 3x^2 + 4x - 5.
- Divide the first term of this new expression (-7x^3) by the first term of the denominator (x). This gives -7x^2.
- Multiply the entire denominator (x + 4) by -7x^2, which gives -7x^3 - 28x^2.
- Subtract this result from the previous expression (-7x^3 - 3x^2 + 4x - 5) to get 25x^2 + 4x - 5.
- Bring down the next term from the numerator, which is 25x^2. Now you have 25x^2 + 4x - 5.
- Divide the first term of this new expression (25x^2) by the first term of the denominator (x). This gives 25x.
- Multiply the entire denominator (x + 4) by 25x, which gives 25x^2 + 100x.
- Subtract this result from the previous expression (25x^2 + 4x - 5) to get -96x - 5.
- Bring down the next term from the numerator, which is -96x. Now you have -96x - 5.
- Divide the first term of this new expression (-96x) by the first term of the denominator (x). This gives -96.
- Multiply the entire denominator (x + 4) by -96, which gives -96x - 384.
- Subtract this result from the previous expression (-96x - 5) to get 379.
- Since there are no more terms in the numerator, the division is complete.
- The quotient is x^3 - 7x^2 + 25x - 96, and the remainder is 379.
Therefore, (x^4 - 3x^2 + 4x - 5) divided by (x + 4) equals x^3 - 7x^2 + 25x - 96 with a remainder of 379.
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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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