The polynomial is given to be:
[tex]27x^3+1000[/tex]
We can rewrite this expression by applying the knowledge of exponents:
[tex]\Rightarrow(3x)^3+10^3[/tex]
Apply the sum of cubes formula:
[tex]x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)[/tex]
Therefore, we have:
[tex]\left(3x\right)^3+10^3=\left(3x+10\right)\left(3^2x^2-10\cdot \:3x+10^2\right)[/tex]
Hence, we can simplify the expression to give the answer:
[tex]27x^3+1000=\left(3x+10\right)\left(9x^2-30x+100\right)[/tex]
The correct option is OPTION B.
