actor the polynomial completely. Do NOT put any spaces in your answers.Must show work/steps on your work page𝑥2−4𝑥+3 =

Sure, let's factor the polynomial $x^2 - 4x + 3$ step by step.

1. Identify the polynomial: $x^2 - 4x + 3$

2. Set up the equation for factoring: We need to find two numbers that multiply to the constant term (3) and add up to the coefficient of the linear term (-4).

3. Find the factors of the constant term (3):

   • The factors of 3 are (1, 3) and (-1, -3).

4. Determine which pair of factors add up to the coefficient of the linear term (-4):

   • The pair (-1, -3) adds up to -4 because $-1 + (-3) = -4$.

5. Write the polynomial as a product of two binomials:

   • Using the factors found, we can write the polynomial as: $x^2 - 4x + 3 = (x - 1)(x - 3)$

6. Verify the factorization:

   • Expand $(x - 1)(x - 3)$ to ensure it equals the original polynomial: $(x - 1)(x - 3) = x^2 - 3x - x + 3 = x^2 - 4x + 3$

So, the completely factored form of the polynomial $x^2 - 4x + 3$ is: $(x-1)(x-3)$