Question

If a polynomial function f(x) has roots 3 and sq root 5 and -6, what must be a factor of f(x)

Answer 1

Step-by-step explanation:

$\text{If}\ a,\ b\ \text{and}\ c\ \text{are the zeros of a polynomial, then we can write this}\\\text{polynomial in form:}\\\\p(x)=(x-a)(x-b)(x-c)\bigg(r(x)\bigg)\\\\\text{where}\ \ r(x)\ \text{is other polynomial or number}.\\\\\text{Therefore}\\\\\text{if a polynomial function}\ f(x)\ \text{has roots (zeros):}\ 3,\ \sqrt5\ \text{and}\ -6,\\\text{then we can write it in form:}\\\\f(x)=(x-3)(x-\sqrt5)(x-(-6)\bigg(r(x)\bigg)\\\\f(x)=(x-3)(x-\sqrt5)(x+6)\bigg(r(x)\bigg)$

$\text{The factors of this polynomial function are:}\\\\x-3,\ x-\sqrt5\ \text{and}\ x+6.$