If 6 x^3+7 x^2-14 x+11 6 x^3+x^2-10 x+3 =a+ b x+p + c q x+3 + d 3 x+p then a+b p+q =

Step-by-step solution

Given that: 6 x^3+7 x^2-14 x+11 6 x^3+x^2-10 x+3 =a+ b x+p + c q x+3 + d 3 x+p ...(i) = 6 x^3+7 x^2-14 x+11 6 x^3+x^2-10 x+3 =1+ 6 x^2-4 x+8 6 x^3+x^2-10 x+3 =1+ 6 x^2-4 x+8 (x-1)(3 x-1)(2 x+3) ...(ii) Now let 6 x^2-4 x+8 (x-1)(3 x-1)(2 x+3) = A (x-1) + B (3 x-1) + C (2 x+3) ...(iii) (6 x^2-4 x+8 )= A (3 x-1)(2 x+3)+ B (x-1)(2 x+3)+ C (x-1)(3 x-1) ...(iv) Put x=1 in equation (iv), we get 14-4=A(2)(5) A=1 Put x= 1 3 in eq ^ n (iv), we get 22 3 = B (- 22 9 ) B =-3 Put x=- 3 2 in equation (iv), we get 55 2 = C. 55 C =