Răspuns:
Explicație pas cu pas:
P(x) = x⁵-7kx²+2x-k ; Q(x) = -x⁵+x²-2x+k
a) S(x) = P(x) + Q(x) = x⁵-7kx²+2x-k -x⁵+x²-2x+k = x²(1-7k)
D(x) = P(x) - Q(x) =x⁵-7kx²+2x-k-(-x⁵+x²-2x+k) =
= x⁵-7kx²+2x-k +x⁵-x²+2x-k = 2x⁵-x²(1+7k)+4x-2k
b) S(x) are gradul 2 ; D(x) are gradul 5
c) P(x) = binom => k = 0 sau k = 1/7
Q(x) = trinom => k = 0 ; k = x⁵ ; k = -x² ; k = 2x
d) S(x) monom de grad 2 => k ∈ R - {1/7}
