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When a polynomial is divided by x_ 1 remainder is 5,if it is divided by x_2 remainder is 7 what is the remainder when the polynomial is divided by (x_1)(x_2)?
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When a polynomial is divided by x_ 1 remainder is 5,if it is divided b...
Solution:
Given, when a polynomial is divided by x1 remainder is 5, and when it is divided by x2 remainder is 7.
Let the polynomial be represented as P(x).
So, we can write:
P(x) = quotient(x)(x1) + 5 ...(1)
P(x) = quotient'(x)(x2) + 7 ...(2)
Finding the Remainder When Divided by (x1)(x2)
To find the remainder when the polynomial is divided by (x1)(x2), we need to rewrite equation (1) and (2) in terms of (x1)(x2).
Multiplying equation (1) by x2, we get:
P(x)x2 = quotient(x)(x1)x2 + 5x2
Multiplying equation (2) by x1, we get:
P(x)x1 = quotient'(x)(x2)x1 + 7x1
Now, multiplying both equations, we get:
P(x)(x1)(x2) = quotient(x)(x1)x2(x1)(x2) + 5x2(x1)(x2)
P(x)(x1)(x2) = quotient'(x)(x2)x1(x1)(x2) + 7x1(x1)(x2)
Adding the above two equations, we get:
P(x)(x1)(x2) = (quotient(x)(x1)x2 + 5x2)(x1)(x2) + (quotient'(x)(x2)x1 + 7x1)(x1)(x2)
P(x)(x1)(x2) = (quotient(x)x2 + 5)(x1)(x2) + (quotient'(x)x1
Given, when a polynomial is divided by x1 remainder is 5, and when it is divided by x2 remainder is 7.
Let the polynomial be represented as P(x).
So, we can write:
P(x) = quotient(x)(x1) + 5 ...(1)
P(x) = quotient'(x)(x2) + 7 ...(2)
Finding the Remainder When Divided by (x1)(x2)
To find the remainder when the polynomial is divided by (x1)(x2), we need to rewrite equation (1) and (2) in terms of (x1)(x2).
Multiplying equation (1) by x2, we get:
P(x)x2 = quotient(x)(x1)x2 + 5x2
Multiplying equation (2) by x1, we get:
P(x)x1 = quotient'(x)(x2)x1 + 7x1
Now, multiplying both equations, we get:
P(x)(x1)(x2) = quotient(x)(x1)x2(x1)(x2) + 5x2(x1)(x2)
P(x)(x1)(x2) = quotient'(x)(x2)x1(x1)(x2) + 7x1(x1)(x2)
Adding the above two equations, we get:
P(x)(x1)(x2) = (quotient(x)(x1)x2 + 5x2)(x1)(x2) + (quotient'(x)(x2)x1 + 7x1)(x1)(x2)
P(x)(x1)(x2) = (quotient(x)x2 + 5)(x1)(x2) + (quotient'(x)x1
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When a polynomial is divided by x_ 1 remainder is 5,if it is divided b...
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When a polynomial is divided by x_ 1 remainder is 5,if it is divided by x_2 remainder is 7 what is the remainder when the polynomial is divided by (x_1)(x_2)?
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When a polynomial is divided by x_ 1 remainder is 5,if it is divided by x_2 remainder is 7 what is the remainder when the polynomial is divided by (x_1)(x_2)? 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 When a polynomial is divided by x_ 1 remainder is 5,if it is divided by x_2 remainder is 7 what is the remainder when the polynomial is divided by (x_1)(x_2)? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a polynomial is divided by x_ 1 remainder is 5,if it is divided by x_2 remainder is 7 what is the remainder when the polynomial is divided by (x_1)(x_2)?.
When a polynomial is divided by x_ 1 remainder is 5,if it is divided by x_2 remainder is 7 what is the remainder when the polynomial is divided by (x_1)(x_2)? 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 When a polynomial is divided by x_ 1 remainder is 5,if it is divided by x_2 remainder is 7 what is the remainder when the polynomial is divided by (x_1)(x_2)? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a polynomial is divided by x_ 1 remainder is 5,if it is divided by x_2 remainder is 7 what is the remainder when the polynomial is divided by (x_1)(x_2)?.
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