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The quotient and remainder are x - 2 and -2x + 4 respectively. If the polynomial x3 - 3x2 + x + 2 is divided by g(x). Find g(x)
- a)x2 + x + 1
- b)x2 - x - 1
- c)x2 - x + 1
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The quotient and remainder are x - 2 and -2x + 4 respectively. If the ...
Given, quotient = x - 2 and remainder = -2x + 4.
So, we know that:
x³ - 3x² + x + 2 = g(x) * (x - 2) - 2x + 4
Let's simplify the right-hand side:
x³ - 3x² + x + 2 = g(x) * x - 2g(x) - 2x + 4
Now, let's rearrange the terms:
x³ - 3x² + x + 2 = g(x) * x - 2x - 2g(x) + 4
x³ - 3x² + x + 2 = (g(x) - 2) * x - 2g(x) + 4
Now, we can equate the coefficients of x², x, and the constant term on both sides to get a system of equations:
Coefficient of x²: -3 = g(x) - 2
Coefficient of x: 1 = g(x)
Constant term: 2 = -2g(x) + 4
Solving the system of equations, we get:
g(x) = 1
-3 = g(x) - 2 = -1
2 = -2g(x) + 4
g(x) = 1
Therefore, the polynomial g(x) is x² - x + 1, which is option C.
So, we know that:
x³ - 3x² + x + 2 = g(x) * (x - 2) - 2x + 4
Let's simplify the right-hand side:
x³ - 3x² + x + 2 = g(x) * x - 2g(x) - 2x + 4
Now, let's rearrange the terms:
x³ - 3x² + x + 2 = g(x) * x - 2x - 2g(x) + 4
x³ - 3x² + x + 2 = (g(x) - 2) * x - 2g(x) + 4
Now, we can equate the coefficients of x², x, and the constant term on both sides to get a system of equations:
Coefficient of x²: -3 = g(x) - 2
Coefficient of x: 1 = g(x)
Constant term: 2 = -2g(x) + 4
Solving the system of equations, we get:
g(x) = 1
-3 = g(x) - 2 = -1
2 = -2g(x) + 4
g(x) = 1
Therefore, the polynomial g(x) is x² - x + 1, which is option C.
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Community Answer
The quotient and remainder are x - 2 and -2x + 4 respectively. If the ...
Hey there...
I tried attaching the answer... but it doesnt seem to work... so hope this helps..
Taking the polynomial x3 - 3x2 + x+ 2 as P(x), quotient as q(x), remainder as r(x) and the divisor (which is to be found) as g(x).
Applying,
g(x) = P(x) - r(x)/ q(x)
You will get a polynomial x3- 3x2+ 3x -2/ x-2
On dividing, the remainder to be obtained here must be zero.
The quotient in this case will give you the divisor which was to be found out...
i. e. x2 - x + 1
Hope you find this useful... have a good day..
I tried attaching the answer... but it doesnt seem to work... so hope this helps..
Taking the polynomial x3 - 3x2 + x+ 2 as P(x), quotient as q(x), remainder as r(x) and the divisor (which is to be found) as g(x).
Applying,
g(x) = P(x) - r(x)/ q(x)
You will get a polynomial x3- 3x2+ 3x -2/ x-2
On dividing, the remainder to be obtained here must be zero.
The quotient in this case will give you the divisor which was to be found out...
i. e. x2 - x + 1
Hope you find this useful... have a good day..
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The quotient and remainder are x - 2 and -2x + 4 respectively. If the polynomial x3 - 3x2 + x + 2 is divided by g(x). Find g(x)a)x2 + x + 1b)x2 - x - 1c)x2 - x + 1d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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The quotient and remainder are x - 2 and -2x + 4 respectively. If the polynomial x3 - 3x2 + x + 2 is divided by g(x). Find g(x)a)x2 + x + 1b)x2 - x - 1c)x2 - x + 1d)none of theseCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The quotient and remainder are x - 2 and -2x + 4 respectively. If the polynomial x3 - 3x2 + x + 2 is divided by g(x). Find g(x)a)x2 + x + 1b)x2 - x - 1c)x2 - x + 1d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The quotient and remainder are x - 2 and -2x + 4 respectively. If the polynomial x3 - 3x2 + x + 2 is divided by g(x). Find g(x)a)x2 + x + 1b)x2 - x - 1c)x2 - x + 1d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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