When 9x2−6x+2 is divided by x, the remainder is

To find the remainder when 9x^2 - 6x + 2 is divided by x, we can use polynomial division.

Step 1: Divide the first term of the numerator (9x^2) by the first term of the denominator (x). This gives us 9x.

Step 2: Multiply the entire denominator (x) by the result from step 1 (9x), which gives us 9x^2. Subtract this from the original numerator, which gives us -6x + 2.

Step 3: Repeat the process with the new numerator (-6x + 2). Divide the first term of the new numerator (-6x) by the first term of the denominator (x), which gives us -6.

Step 4: Multiply the entire denominator (x) by the result from step 3 (-6), which gives us -6x. Subtract this from the new numerator, which gives us 2.

Step 5: Since the degree of the new numerator (2) is less than the degree of the denominator (x), we stop here. The remainder is 2.