Question

Die polinomul P(x)=x^3-x^2+ax+4. a)sa se afle a aprtine R,astfel incat P(1)=0. b)pentru a determinat abterior,descompuneti polinomul P(x) in factori.

Answer 1

P(1)=1-1+a+4
P(1)=a+4
p(1)=0⇒a+4=0⇒a=-4
$P(x)= x^{3}- x^{2} -4x+4 \\ P(x)= x^{2} (x-1)-4(x-1)=(x-1)( x^{2} -4)=(x-1)(x-2)(x+2)$

Answer 2

P(x)=x³-x²+ax+4
P(1)=1³-1²+a+4=a+4
a+4=0
a=-4
P(x)=x³-x²-4x+4=x²(x-1)-4(x-1)=(x-1)(x²-4)=(x-1)(x-2)(x+2)