Question

select the correct answer.
one factor of the polynomial ( x^3 - 7x^2 + 13x - 3 ) is ( (x - 3) ). what is the other factor of the polynomial? (note: use long or synthetic division.)
a. ( (x^2 + 4x - 1) )
b. ( (x^2 - 4x + 1) )
c. ( (x - 4) )
d. ( (x + 4) )

Explanation:

Step1: Use polynomial division (synthetic division here since the divisor is \(x - 3\))

The polynomial is \(x^3 - 7x^2 + 13x - 3\), and the divisor is \(x - 3\). For synthetic division, we use the root \(x = 3\).
Set up synthetic division:

$$
LATEXBLOCK0
$$

Step2: Interpret the result

The coefficients of the quotient polynomial from synthetic division are \(1, -4, 1\), so the quotient is \(x^2 - 4x + 1\).

Answer:

B. \((x^2 - 4x + 1)\)