Factors of x³ − 7x + 6
The factors of \[ x^3-7x+6 \] are
(a) \(x(x-6)(x-1)\)
(b) \((x^2-6)(x-1)\)
(c) \((x+1)(x+2)(x-3)\)
(d) \((x-1)(x+3)(x-2)\)
Solution
\[ x^3-7x+6 \]
\[ =x^3-x^2+x^2-7x+6 \]
\[ =x^2(x-1)+x(x-1)-6(x-1) \]
\[ =(x-1)(x^2+x-6) \]
\[ =(x-1)(x+3)(x-2) \]
Therefore,
\[ \boxed{(d)\ (x-1)(x+3)(x-2)} \]