If x is real and (x)= | array ccc x^2+x & 2 x-1 & x+3 3 x+1 & x^2+2 & x^3-3 x-3 & x^2+4 & 2 x array |=a₀ x^7+a₁ x^6+a₂ x^5+ +a₆ x+a₇ , then:

Step-by-step solution

(1) a₇= (0)= | array ccc 0 & -1 & 3 1 & 2 & -3 -3 & 4 & 0 array |=21 (2) and (4) (1)= | array ccc 2 & 1 & 4 4 & 3 & -2 -2 & 5 & 2 array |=132= _ k=0 ^7 a_k Now, _ k=0 ^6 a_k= _ k=0 ^7 a_k-a₇=132-21=111 (3) (-1)= | array ccc 0 & -3 & 2 -2 & 3 & -4 -4 & 5 & -2 array |=-32