Question

Bantuin yaa..

Jika suku banyak P(x) = 2x4 + ax3 + 5x + b dibagi oleh (x2 -1) member sisa 6x + 5, maka a.b =

Answer 1

P(x)= 2x^4+ax^3+5x+b         
x^2-1 = (x-1) (x+1)
sisa 6x+5
x=1 dan x=-1
P(1)= 2(1)^4+a(1)^3+5(1)+b= 6(1)+5
= 2+a+5+b=11
=a+b=4
P(-1)= 2(-1)^4+a(-1)^3+5(-1)+b=6(-1)+5
=2-a-5+b=-1
-a+b=2

eleminasikan
a+b=4
-a+b=2  (coret b)
2a=2
a=1
b=3 dari a+b=4 ⇒ 1+b=4⇒ b=4-1 ⇒b = 3
a.b= 1x3=3