Question

Which of the following is the correct factorization of the polynomial below?27x^3+1000

Answer 1

The polynomial is given to be:

`27x^3+1000`

We can rewrite this expression by applying the knowledge of exponents:

`\Rightarrow(3x)^3+10^3`

Apply the sum of cubes formula:

`x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)`

Therefore, we have:

`\left(3x\right)^3+10^3=\left(3x+10\right)\left(3^2x^2-10\cdot \:3x+10^2\right)`

Hence, we can simplify the expression to give the answer:

`27x^3+1000=\left(3x+10\right)\left(9x^2-30x+100\right)`

The correct option is OPTION B.