Answer:
The following polynomial can be factorized as,
f(x) = [tex](x-4)(x-3)(x+2)[/tex]
Step-by-step explanation:
It is given that at x = -2, the value of polynomial is zero, thus, by factor theorm,
(x+2) is the factor of the above polynomial.
By dividing the given polynomial by (x+2), we get,
F(x) = [tex](x-4)(x^{2} -7x +12)[/tex]
This can be further simplified as,
[tex](x^{2} -7x +12)[/tex] = [tex](x^{2} -4x-3x+12)[/tex]
= [tex](x(x-4)-3(x-4))[/tex]= [tex](x-3)(x-4)[/tex]
Thus the polynomial becomes,
f(x) = [tex](x-4)(x-3)(x+2)[/tex]
