Question

If \( (x - a) \) is a factor of \( x^6 - ax^5 + x^4 - ax^3 + 3x - a + 2 \), then the value of \( a \) is:

• A. 1
• B. 0
• C. -1
• D. 2

Hint:

When given a factor of a polynomial, substitute the value that makes the factor 0 into the polynomial and solve for the unknown variable.

Answer 1

The Correct Option is C

Step 1: Since \( (x - a) \) is a factor, substituting \( x = a \) into the polynomial should make the expression equal to 0. \[ a^6 - a \cdot a^5 + a^4 - a \cdot a^3 + 3a - a + 2 = 0 \] Step 2: Simplify the equation: \[ a^6 - a^6 + a^4 - a^4 + 3a - a + 2 = 0 \] \[ 2a + 2 = 0 \] Step 3: Solve for \( a \): \[ a = -1 \] Thus, the value of \( a \) is -1.