Factor x^3 - 6x^2 + 11x - 6.

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Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

Multiple Choice

Factor x^3 - 6x^2 + 11x - 6.

Explanation:
Finding where the expression equals zero and writing the polynomial as a product of linear factors. If you plug in 1, you get 1 - 6 + 11 - 6 = 0, so x - 1 is a factor. Dividing the cubic by (x - 1) gives x^2 - 5x + 6. That quadratic factors nicely as (x - 2)(x - 3). Multiplying back together, (x - 1)(x - 2)(x - 3) expands to x^3 - 6x^2 + 11x - 6, which matches the original expression. So the factorization is (x - 1)(x - 2)(x - 3).

Finding where the expression equals zero and writing the polynomial as a product of linear factors. If you plug in 1, you get 1 - 6 + 11 - 6 = 0, so x - 1 is a factor. Dividing the cubic by (x - 1) gives x^2 - 5x + 6. That quadratic factors nicely as (x - 2)(x - 3). Multiplying back together, (x - 1)(x - 2)(x - 3) expands to x^3 - 6x^2 + 11x - 6, which matches the original expression. So the factorization is (x - 1)(x - 2)(x - 3).

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