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Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided by x-3 leaves ba remainder -22?
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Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided ...
Introduction:
To find out the value of k, we need to divide the polynomial p(x) by (x-3) and obtain the remainder. Then we can equate that remainder to -22 and solve for k.
Synthetic Division:
Synthetic division is a shortcut method to divide a polynomial by a linear factor (x-a). It involves writing the coefficients of the polynomial in a specific pattern and performing a series of operations to obtain the quotient and remainder.
Writing the Polynomial:
Let's write the polynomial p(x) in the standard form with all the coefficients and exponents in place.
p(x) = kx^3 + 9x^2 + 4x - 10
Synthetic Division:
Let's perform synthetic division by (x-3) to obtain the remainder.
3 | k 9 4 -10
| 3 36 120
|______________
k 12 40 110
The remainder is 110, which is not equal to -22. This means that the value of k is such that the remainder is not -22 when p(x) is divided by (x-3).
Conclusion:
Since the remainder is not -22, there is no value of k that satisfies the given condition. Therefore, we cannot find the value of k.
To find out the value of k, we need to divide the polynomial p(x) by (x-3) and obtain the remainder. Then we can equate that remainder to -22 and solve for k.
Synthetic Division:
Synthetic division is a shortcut method to divide a polynomial by a linear factor (x-a). It involves writing the coefficients of the polynomial in a specific pattern and performing a series of operations to obtain the quotient and remainder.
Writing the Polynomial:
Let's write the polynomial p(x) in the standard form with all the coefficients and exponents in place.
p(x) = kx^3 + 9x^2 + 4x - 10
Synthetic Division:
Let's perform synthetic division by (x-3) to obtain the remainder.
3 | k 9 4 -10
| 3 36 120
|______________
k 12 40 110
The remainder is 110, which is not equal to -22. This means that the value of k is such that the remainder is not -22 when p(x) is divided by (x-3).
Conclusion:
Since the remainder is not -22, there is no value of k that satisfies the given condition. Therefore, we cannot find the value of k.
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Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided by x-3 leaves ba remainder -22?
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Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided by x-3 leaves ba remainder -22? 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 Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided by x-3 leaves ba remainder -22? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided by x-3 leaves ba remainder -22?.
Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided by x-3 leaves ba remainder -22? 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 Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided by x-3 leaves ba remainder -22? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of k if the polynomial p(x)= kx^3 9x2 4x-10 is divided by x-3 leaves ba remainder -22?.
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