Given that \(3x^2-2x+4=A(x-1)^2+B(x-1)+C\) for all values of \(x\), find the values of \(A\), \(B\) and \(C\).[3]
A polynomial \(f(x)\) can be written in the form \(f(x)=Q(x)(x-1)(x-2)+Ax+B\), where \(Q(x)\) is a polynomial and \(A\) and \(B\) are constants. When \(f(x)\) is divided by \((x-1)\), the remainder is 3 and when \(f(x)\) is divided by \((x-2)\), the remainder is 4. Find the remainder when \(f(x)\) is divided by \((x-1)(x-2)\).[4]
If \(x+y=5\) and \(xy=6\), find the value of
\(x^2+y^2\),[2]
\(x^3+y^3\).[2]
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.
Answer:(a) \(A=3,B=4,C=5\). (b) \(x+2\). (c)(i) 13. (ii) 35.