Maths · Polynomial, rational, trigonometric, logarithmic and exponential functions
If the quotient of When divided by 12) is , then the descending order of is
If the quotient of \( x^{4}-11 x^{3}+44 x^{2}- \) \( 76 x+48 . \) When divided by \( \left(x^{2}-7 x+\right. \) 12) is \( A x^{2}+B x+C \), then the descending order of \( A, B, C \) is
- A. \( A, B, C \)
- B. \( B, C, A \)
- C. \( A, C, B \)
- D. \( C, A, B \)
Step-by-step solution
Perform polynomial division of x^4 - 11x^3 + 44x^2 - 76x + 48 by x^2 - 7x + 12. The quotient is x^2 - 4x + 4, so A=1, B=-4, C=4. Descending order (largest to smallest) is C=4, A=1, B=-4, i.e., C, A, B, which corresponds to option D.