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What do you mean by reminder theorem and factor theorem? give an example also .?
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What do you mean by reminder theorem and factor theorem? give an examp...
The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a). In other words, if you want to evaluate the function f(x) for a given number, a, you can divide that function by x - a and your remainder will be equal to f(a).
Example:
Examine whether x + 2 is a factor of x3 + 3x2 + 5x + 6.
Solution: To begin with, we know that the zero of the polynomial (x + 2) is –2. Let p(x) = x3 + 3x2 + 5x + 6
Then, p(–2) = (–2)3 + 3(–2)2 + 5(–2) + 6 = –8 + 12 – 10 + 6 = 0
According to the factor theorem, if p(a) = 0, then (x – a) is a factor of p(x). In this example, p(a) = p(- 2) = 0
Therefore, (x – a) = {x – (-2)} = (x + 2) is a factor of ‘x3 + 3x2 + 5x + 6’ or p(x).
Example:
Examine whether x + 2 is a factor of x3 + 3x2 + 5x + 6.
Solution: To begin with, we know that the zero of the polynomial (x + 2) is –2. Let p(x) = x3 + 3x2 + 5x + 6
Then, p(–2) = (–2)3 + 3(–2)2 + 5(–2) + 6 = –8 + 12 – 10 + 6 = 0
According to the factor theorem, if p(a) = 0, then (x – a) is a factor of p(x). In this example, p(a) = p(- 2) = 0
Therefore, (x – a) = {x – (-2)} = (x + 2) is a factor of ‘x3 + 3x2 + 5x + 6’ or p(x).
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What do you mean by reminder theorem and factor theorem? give an example also .?
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What do you mean by reminder theorem and factor theorem? give an example also .? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What do you mean by reminder theorem and factor theorem? give an example also .? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What do you mean by reminder theorem and factor theorem? give an example also .?.
What do you mean by reminder theorem and factor theorem? give an example also .? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What do you mean by reminder theorem and factor theorem? give an example also .? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What do you mean by reminder theorem and factor theorem? give an example also .?.
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