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One factor of the polynomial 2x^3-3x²- 3x + 2is (x - 2). Which expression represents the other factor, or factors, of the polynomial?

A. (2x - 1)(x + 1)
B. (2x² + 1)
C. (2x²-x+ 1)
D. (2x + 1)(x - 1)

User EJC
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1 Answer

5 votes

Answer: (2x + 1)(x - 1)

Explanation:

We can use polynomial long division or synthetic division to find the other factor of the polynomial. Alternatively, we can use the fact that if (x - 2) is a factor of the polynomial 2x^3 - 3x^2 - 3x + 2, then (2 - x) is also a factor of the polynomial.

We can use synthetic division to divide the polynomial by (2 - x) and obtain the quotient polynomial:

2 -3 -3 2

2-x | 2 -3 -3 2

- 4 14 -22

2 -7 11 0

Therefore, the other factor of the polynomial is 2x^2 - 7x + 11. We can factor this quadratic expression as (2x + 1)(x - 1).

Thus, the factorization of the polynomial 2x^3 - 3x^2 - 3x + 2 is:

2x^3 - 3x^2 - 3x + 2 = (x - 2)(2x + 1)(x - 1)

User Tamer Hussien
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