If f(x)= | array ccc x-3 & 2 x^2-18 & 2 x^3-81 x-5 & 2 x^2-50 & 4 x^3-500 1 & 2 & 3 array | then f(1) f(3)+f(3) f(5)+f(5) f(1) is

Step-by-step solution

f(x)=2(x-5) | array ccc x-3 & x^2-9 & 2 x^3-81 1 & x+5 & 4 (x^2+5 x+25 ) 1 & 1 & 3 array | f(5)=0 and f(1)=2(-4) [ array ccc -2 & -8 & -79 1 & 6 & 124 1 & 1 & 3 array ]=-8[212-968+395]=2888f(3)=2(-2) [ array ccc 0 & 0 & -27 1 & 8 & 196 1 & 1 & 3 array ]=-4[0+0-27(1-8)]=-756 So, f(1) f(3)+f(3) f(5)+f(5) f(1)=2888 (-756)+0+0=-2183328