Question

$\text{If}(x-3)\text{and}(x-2)\text{are two factors of the polynomial}{x}^3-6x^2+11x-6,\text{then find the third factor.}$

Answer 1

Since (x-3) and (x-2) are the factors of the given polynomial, the product of (x-3) and (x-2)
$(x-3)(x-2)$
$=x^2-2x-3x+6$
$=x^2-5x+6\text{will also be a factor of the polynomial.}$
Now, for finding the third factor, divide the polynomial
$x^3-6x^2+11x-6\text{by}(x^2-5x+6).$
The quotient is x - 1 and the remainder is 0.
So the third factor is (x - 1) of given polynomial.