Question

4. Use the Factor Theorem to determine whether glx) is
following cases :
(i) f(x) = 5x + x2 - 5x - 1, g(x) = x + 1
(ii) f(x) = x3 + 3 x2 + 3x + 1, g(x) = x + 1​

Answer 1

I)x+1=0
x=-1
f(x)=5(-1)+(-1)^2-5(-1)-1
= -5+1+5-1
= 0
On substituting the value of x as -1,f(x) is 0.Therefore,g(x) is a factor of f(x)
ii)x+1=0
x = -1
On substituting the value of x as -1,
f(x) = (-1)^3+3(-1)^2+3(-1)+1
= -1+3-3+1
= 0
On substituting the value of x as -1,f(x) is 0.Hence,g(x) is a factor of f(x)