Question

$(x + 2)$
is a factor of the polynomial solve this by factor thearem
$x {}^ {3} - x { }^{2} + 4$
​

Answer 1

Let, f(x) = x³–x²+4

Then, according to the Factor Theorem,

say, g(x)=x+2 is a factor of f(x) if and only if f(Root[g(x)]) = f(–2) = 0

Check if f(–2) ≟ 0

f(–2) = (–2)³–(–2)²+4

f(–2) = –8 –4 + 4 = –8

As, f(–2)≠0

Thus, x+2 is not a factor of x³–x²+4