Math Problem Statement

Phân tích đa thức x^3 - 3x^2 + 3x - 1 thành nhân tử ta được:

Solution

The image you uploaded is a Vietnamese mathematical expression asking to factorize the cubic polynomial x33x2+3x1x^3 - 3x^2 + 3x - 1.

Let's factor the polynomial step by step.

We begin by noticing that the polynomial has the form: x33x2+3x1x^3 - 3x^2 + 3x - 1 This resembles the expanded form of (x1)3(x - 1)^3, as: (x1)3=x33x2+3x1(x - 1)^3 = x^3 - 3x^2 + 3x - 1 Thus, the factorization of x33x2+3x1x^3 - 3x^2 + 3x - 1 is: (x1)3(x - 1)^3

Would you like further clarification on the factorization process, or do you have any other questions?

Here are 5 related questions for further exploration:

  1. How can you confirm if a factorization is correct using polynomial division?
  2. What are the possible roots of cubic polynomials, and how can we find them?
  3. How do we use synthetic division to factorize a polynomial?
  4. What are the differences between factoring linear, quadratic, and cubic polynomials?
  5. How does the Fundamental Theorem of Algebra help in solving cubic equations?

Tip: Always look for patterns, such as perfect cubes, when factoring cubic polynomials.

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Math Problem Analysis

Mathematical Concepts

Algebra
Cubic Polynomials
Factorization

Formulas

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

Theorems

Factorization of Cubic Polynomials

Suitable Grade Level

Grades 9-12