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.