Reduc x^3 - x^2
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x^4
Is it x-1
_____
x^2 Is this right?
yes
To find the quotient of the given expression, "Reduc x^3 - x^2" divided by "x^4," you can apply polynomial division. Here's how you can do it step by step:
Step 1: Arrange the polynomial expression in descending order of exponents.
The given expression is: x^3 - x^2.
Step 2: Write the divisor (x^4) and the dividend (x^3 - x^2) in a long division format.
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x^4 | x^3 - x^2
Step 3: Divide the first term of the dividend (x^3) by the first term of the divisor (x^4), which results in x^(3 - 4) = x^(-1) = 1/x.
Step 4: Multiply the divisor (x^4) by the quotient obtained in the previous step (1/x). This gives you (x^4 * (1/x)) = x^(4 - 1) = x^3.
Step 5: Subtract the result from step 4 (x^3) from the original dividend (x^3 - x^2). This gives you: (x^3 - x^2) - x^3 = -x^2.
Step 6: Bring down the next term from the original dividend (-x^2). Now, the new dividend becomes -x^2.
Step 7: Repeat steps 3-6 until all terms are divided.
Step 8: The quotient obtained from the long division process is x - 1/x.
Therefore, the correct expression after reducing is (x - 1)/x.
In this particular case, when you simplify the expression (x - 1)/x further, it becomes (1/x)(x - 1), which is equivalent to 1 - 1/x. So, it seems that the expression you mentioned, (x - 1)/x^2, is incorrect. The correct reduced form is (x - 1)/x.