Find the remainder when `x^3-a x^2+6x-a` is divided by `x-a`.
Text Solution
AI Generated Solution
To find the remainder when the polynomial \( P(x) = x^3 - ax^2 + 6x - a \) is divided by \( x - a \), we can use the Remainder Theorem. According to the Remainder Theorem, the remainder of the division of a polynomial \( P(x) \) by \( x - c \) is equal to \( P(c) \).
### Step-by-Step Solution:
1. **Identify the polynomial and the divisor**:
We have the polynomial \( P(x) = x^3 - ax^2 + 6x - a \) and we are dividing it by \( x - a \).
2. **Substitute \( x = a \) into the polynomial**:
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