Question

The number of common factor(s) to two polynomials x² − 9 and x³ − x² − 9x + 9 is ______.

Options

• one

• two

• three

Answer 1

The number of common factor(s) to two polynomials x² − 9 and x³ − x² − 9x + 9 is two.

Explanation:

Factorizing x² − 9,

⇒ (x + 3)(x − 3)

Factorizing x³ − x² − 9x + 9,

⇒ x²(x − 1) − 9(x - 1)

⇒ (x² − 9)(x − 1)

⇒ (x + 3)(x − 3)(x − 1)

The number of common factor(s) of two polynomials x² − 9 and x³ - x² − 9x + 9 are two i.e.,(x + 3) and (x − 3).