Question

Mark the correct alternative in each of the following: The factors of $x^3-7x+6$, are

• A. $(x^2-6)(x-1)$
• B. $(x+1)(x+2)(x-3)$
• C. $(x-1)(x+3)(x-2)$
• D. $x(x-6)(x-1)$

Answer 1

The correct option is C $(x-1)(x+3)(x-2)$

Given: $x^3-7x+6$

$\therefore x^3-7x+6$

$=x^3-x-6x+6$

$=x(x^2-1)-6(x-1)$

$=x(x-1)(x+1)-6(x-1)$

$[\because a^2-b^2=(a+b\left)\right(a-b\left)\right]$

$=(x-1)\left[x\right(x+1)-6]$

$=(x-1)[x^2+x-6]$

$=(x-1)[x^2+3x-2x-6]$

$=(x-1)\left[x\right(x+3)-2(x+3\left)\right]$

$=(x-1)(x+3)(x-2)$

Hence, option $\left(D\right)$ is the correct answer.