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# Which of the following is a factor of 8x^{3} + 1331?

2x - 11

4x^{2} + 22x + 121

4x^{2} - 44x + 121

None of the above

**Solution:**

The equation 8x^{3} + 1331 can be written as

(2x)^{3} + (11)^{3}

Which is of the form a^{3} + b^{3} .

Now,

a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})

Therefore

(2x)^{3} + (11)^{3} = (2x + 11){(2x)^{2} - (2x)(11) +(11)^{2}}

= (2x + 11)(4x^{2} - 22x + 121)

Hence the two factors are (2x + 11) and (4x² - 22x + 121)

Therefore the answer to the question is none of the above.

## Which of the following is a factor of 8x^{3} + 1331?

**Summary:**

“None of the above” choice is a factor of 8x^{3} + 1331.

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