Question

Which of the following statements is a valid polynomial identity?

Statement 1: x3 + 216 = (x − 6)(x2 + 6x + 36)
Statement 2: x3 + 216 = (x + 6)(x2 − 6x + 36)

Group of answer choices

Only statement 1 is valid.

Only statement 2 is valid.

Statement 1 and statement 2 are valid.

Statement 1 and statement 2 are invalid.

Answer 1

Only statement 2 is valid

Explanation:

Let's see how

`\\ \rm\rightarrowtail x^3+216`

`\\ \rm\rightarrowtail x^2+6^3`

`\\ \rm\rightarrowtail (x+6)(x^2-6x+36)`

Hence verified

Answer 2

• B. Only statement 2 is valid.

Explanation:

Using identities

• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)

Applying to the given statements, we can see the second one is valid.

Correct choice is B