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Using remainder theoram find the remainder when x^3 - x^2 x-1 is divided by x-1?
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Using remainder theoram find the remainder when x^3 - x^2 x-1 is divi...
Using Remainder Theorem to Find the Remainder
Understanding the Remainder Theorem is crucial when it comes to finding the remainder of a polynomial when divided by another polynomial. In this case, we are given the polynomial \(x^3 - x^2 + x - 1\) and we want to find the remainder when it is divided by \(x - 1\).
Applying the Remainder Theorem
The Remainder Theorem states that when a polynomial \(f(x)\) is divided by \(x - a\), the remainder is \(f(a)\). In our case, \(a = 1\), so we need to find \(f(1)\).
Substitute x = 1 into the Polynomial
By substituting \(x = 1\) into the polynomial \(x^3 - x^2 + x - 1\), we get:
\(1^3 - 1^2 + 1 - 1 = 1 - 1 + 1 - 1 = 0\)
Interpreting the Result
The remainder we obtained is 0, which means that \(x - 1\) is a factor of the polynomial \(x^3 - x^2 + x - 1\). This implies that the given polynomial is evenly divisible by \(x - 1\), with no remainder.
Therefore, when \(x^3 - x^2 + x - 1\) is divided by \(x - 1\), the remainder is 0.
Understanding the Remainder Theorem is crucial when it comes to finding the remainder of a polynomial when divided by another polynomial. In this case, we are given the polynomial \(x^3 - x^2 + x - 1\) and we want to find the remainder when it is divided by \(x - 1\).
Applying the Remainder Theorem
The Remainder Theorem states that when a polynomial \(f(x)\) is divided by \(x - a\), the remainder is \(f(a)\). In our case, \(a = 1\), so we need to find \(f(1)\).
Substitute x = 1 into the Polynomial
By substituting \(x = 1\) into the polynomial \(x^3 - x^2 + x - 1\), we get:
\(1^3 - 1^2 + 1 - 1 = 1 - 1 + 1 - 1 = 0\)
Interpreting the Result
The remainder we obtained is 0, which means that \(x - 1\) is a factor of the polynomial \(x^3 - x^2 + x - 1\). This implies that the given polynomial is evenly divisible by \(x - 1\), with no remainder.
Therefore, when \(x^3 - x^2 + x - 1\) is divided by \(x - 1\), the remainder is 0.
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Using remainder theoram find the remainder when x^3 - x^2 x-1 is divided by x-1?
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Using remainder theoram find the remainder when x^3 - x^2 x-1 is divided by x-1? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Using remainder theoram find the remainder when x^3 - x^2 x-1 is divided by x-1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using remainder theoram find the remainder when x^3 - x^2 x-1 is divided by x-1?.
Using remainder theoram find the remainder when x^3 - x^2 x-1 is divided by x-1? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Using remainder theoram find the remainder when x^3 - x^2 x-1 is divided by x-1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using remainder theoram find the remainder when x^3 - x^2 x-1 is divided by x-1?.
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