Factor x^2-4x+3

Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.

Expression

Answer

(x - 3)(x - 1)

To factor the trinomial x^2-4x+3, find two numbers that multiply to the constant term and add to the coefficient of x.

x²-4x+3

Step 1 — Factor x² − 4x + 3

Identify the coefficients: a = 1, b = -4, c = 3

Step 2 — Find the factor pair

For a trinomial x² + bx + c, we need two numbers p and q where:

p × q = 3 (the constant term)

p + q = -4 (the coefficient of x)

This works because (x + p)(x + q) = x² + (p+q)x + pq.

-3 × -1 = 3, -3 + (-1) = -4 → use -3 and -1

Step 3 — Split the middle term

Rewrite −4x as −3x and −x:

x² − 3x − x + 3

Step 4 — Factor by grouping

(x² - 3x) + (3 - x)

Factor the GCF from each group:

(x² - 3x) = x(x - 3)

(3 - x) is already in the form 1 · (common factor)

Both groups share the same binomial factor — pull it out:

= (x - 3)(x - 1)

(x - 3)(x - 1)

How to factor x^2-4x+3

To factor x^2-4x+3, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 3)(x - 1).

This is a polynomial factoring problem — we break a polynomial into a product of simpler expressions. Common methods include GCF extraction, difference of squares, and trinomial factoring.

Frequently asked questions

What is the answer to x^2-4x+3?
The answer is (x - 3)(x - 1).

What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.