Question

If $f\left(x\right)=x^6-10x^5-10x^4-10x^3-10x^2-10x+10$, the value of $f\left(11\right)$ is

• A. $1$
• B. $10$
• C. $11$
• D. $21$

Answer 1

The correct option is D $21$

The given expression $f\left(x\right)=x^6-10x^5-10x^4-10x^3-10x^2-10x+10$ can be rewritten as

$f\left(x\right)=x^6-10(x^5+x^4+x^3+x^2+x-1)$.

Now, substitute $x=11$ in the above expression as shown below:

$\Rightarrow f\left(x\right)=x^6-10(x^5+x^4+x^3+x^2+x-1)$

$\Rightarrow f\left(11\right)={11}^6-10({11}^5+{11}^4+{11}^3+{11}^2+11-1)$

$\Rightarrow f\left(11\right)=1771561-10(161051+14641+1331+121+11-1)$

$\Rightarrow f\left(11\right)=1771561-(10\times 177154)$

$\Rightarrow f\left(11\right)=1771561-1771540$

$\Rightarrow f\left(11\right)=21$

Hence, $f\left(11\right)=21$.