2x³-x²-4x+2/ x²-2
To simplify the fraction (2x³ - x² - 4x + 2) / (x² - 2), we can use polynomial long division. Here's how we do it:
Step 1: Ensure that both the numerator and the denominator are written in descending powers of x. Arrange the terms in order of decreasing power:
(2x³ - x² - 4x + 2) / (x² - 2)
Step 2: Divide the highest power term of the numerator (2x³) by the highest power term of the denominator (x²). The result becomes the first term of the simplified expression:
2x³ / x² = 2x
Step 3: Multiply the entire denominator (x² - 2) by the value obtained in step 2 (2x) and subtract it from the numerator (2x³ - x² - 4x + 2):
(2x³ - x² - 4x + 2) - (2x * (x² - 2))
Step 4: Simplify the expression obtained in step 3:
(2x³ - x² - 4x + 2) - (2x³ - 4x) = -x² + 2x + 2
Step 5: Repeat steps 2-4 until there are no more terms left in the numerator or the degree of the numerator is less than the degree of the denominator.
In this case, we cannot proceed further as the degree of the remaining polynomial (-x² + 2x + 2) is less than the degree of the denominator (x² - 2).
Therefore, the simplified expression is 2x with a remainder of (-x² + 2x + 2) / (x² - 2).
Does your expression mean:
2 x³ - x² - 4 x + 2 / x² - 2
or
2 x³ - x² - 4 x + 2 / ( x² - 2 )
and what is your question?