What Is The Remainder When X4+36 Is Divided By X2-8, When we are given a polynomial expression to divide by another polynomial expression, we use the, General, what-is-the-remainder-when-x436-is-divided-by-x2-8, JPOSE
When we are given a polynomial expression to divide by another polynomial expression, we use the method of long division to get the quotient and remainder. In this case, we are asked to find the remainder when X^4+36 is divided by X^2-8.
Let us begin by setting up the long division problem as shown below:
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X^2-8 | X^4 + 0X^3 + 0X^2 + 0X + 36
We start by dividing the first term in the dividend, which is X^4, by the first term in the divisor, which is X^2. This gives us X^2. We then multiply X^2 with the divisor and write the product below the dividend, as shown below:
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X^2-8 | X^4 + 0X^3 + 0X^2 + 0X + 36
- X^4 + 8X^2
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-8X^2 + 0X
Next, we bring down the next term from the dividend, which is 0X^2. We then divide -8X^2 by X^2, which gives us -8. We write -8 above the dividend and multiply -8 with the divisor, as shown below:
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X^2-8 | X^4 + 0X^3 + 0X^2 + 0X + 36
- X^4 + 8X^2
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-8X^2 + 0X
-8X^2 + 64
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-64
We then bring down the next term from the dividend, which is 0X. We divide -64 by X^2, which gives us -64/X^2. However, since the divisor does not contain an X term, we cannot proceed any further with the long division method.
Therefore, the remainder when X^4+36 is divided by X^2-8 is -64.
In conclusion, we used the long division method to find the remainder when X^4+36 is divided by X^2-8. The remainder is -64.