Find the quotient and remainder using long division. $$ \frac{9 x^{2}-x+5}{3 x^{2}-9 x} $$ quotient Check which variable(s) should be in your answer.

Question

UpStudy AI · Accepted Answer

To perform the long division of (9x² – x + 5) by (3x² – 9x):

1. Divide the leading term of the numerator by the leading term of the denominator:
  9x² ÷ 3x² = 3.
  So the quotient is 3.

2. Multiply the entire divisor by 3:
  3 × (3x² – 9x) = 9x² – 27x.

3. Subtract this from the original numerator:
  (9x² – x + 5) – (9x² – 27x) = 9x² – x + 5 – 9x² + 27x = 26x + 5.
  This is the remainder.

Thus, the division can be expressed as:
  (9x² – x + 5) ÷ (3x² – 9x) = 3 with a remainder of 26x + 5.

Note: The quotient is just the constant 3 (it contains no x), while the remainder is expressed in terms of x.

Final Answer:
 Quotient: 3
 Remainder: 26x + 5
Quotient: 3 Remainder: 26x + 5

Find the quotient and remainder using long division. \[ \frac{9 x^{2}-x+5}{3 x^{2}-9 x} \] quotient Check which variable(s) should be in your answer.