Question

The minimum value of the polynomial $x\left(x+1\right)\left(x+2\right)\left(x+3\right)$ is

• A. $0$
• B. $\frac{9}{\begin{array}{c}16\end{array}}$
• C. $-1$
• D. $-\frac{3}{2}$

Answer 1

The correct option is C $-1$

Given,

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

$=x(x^2+3x+2)(x+3)$

$=x(x^3+6x^2+11x+6)$

$=x^4+6x^3+11x^2+6x$

use trial and error method,

let us put $x=-1$

we have,

$=(-1{)}^4+6(-1{)}^3+11(-1{)}^2+6(-1)$

$=1-6+11-6=0$

$\therefore x=-1$ is the correct option