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If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided by (x -3) then the remainder in each case is same. Find value of p. Plz answer this question ?
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If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided...
Polynomial p(x) 3x-4 And equation the questions I see (xcube - 4x) ( x- 3) = x square 3x +12x / x-3
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If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided...
Understanding the Problem
To find the value of p such that the remainders when the polynomials pxcube + 4xsquare + 3x - 4 and xcube - 4x + p are divided by (x - 3) are the same, we will use the Remainder Theorem.
Step 1: Apply the Remainder Theorem
According to the Remainder Theorem, the remainder of a polynomial f(x) when divided by (x - a) is f(a).
- For the first polynomial:
f(x) = pxcube + 4xsquare + 3x - 4
R1 = f(3) = p(3)^3 + 4(3)^2 + 3(3) - 4
- For the second polynomial:
g(x) = xcube - 4x + p
R2 = g(3) = (3)^3 - 4(3) + p
Step 2: Calculate R1
- R1 = p(27) + 4(9) + 9 - 4
- R1 = 27p + 36 + 9 - 4
- R1 = 27p + 41
Step 3: Calculate R2
- R2 = 27 - 12 + p
- R2 = 15 + p
Step 4: Set R1 equal to R2
Since R1 = R2, we have:
27p + 41 = 15 + p
Step 5: Solve for p
- Rearranging the equation:
27p - p = 15 - 41
26p = -26
p = -1
Conclusion
The value of p that satisfies the condition is -1.
To find the value of p such that the remainders when the polynomials pxcube + 4xsquare + 3x - 4 and xcube - 4x + p are divided by (x - 3) are the same, we will use the Remainder Theorem.
Step 1: Apply the Remainder Theorem
According to the Remainder Theorem, the remainder of a polynomial f(x) when divided by (x - a) is f(a).
- For the first polynomial:
f(x) = pxcube + 4xsquare + 3x - 4
R1 = f(3) = p(3)^3 + 4(3)^2 + 3(3) - 4
- For the second polynomial:
g(x) = xcube - 4x + p
R2 = g(3) = (3)^3 - 4(3) + p
Step 2: Calculate R1
- R1 = p(27) + 4(9) + 9 - 4
- R1 = 27p + 36 + 9 - 4
- R1 = 27p + 41
Step 3: Calculate R2
- R2 = 27 - 12 + p
- R2 = 15 + p
Step 4: Set R1 equal to R2
Since R1 = R2, we have:
27p + 41 = 15 + p
Step 5: Solve for p
- Rearranging the equation:
27p - p = 15 - 41
26p = -26
p = -1
Conclusion
The value of p that satisfies the condition is -1.
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If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided by (x -3) then the remainder in each case is same. Find value of p. Plz answer this question ? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided by (x -3) then the remainder in each case is same. Find value of p. Plz answer this question ? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided by (x -3) then the remainder in each case is same. Find value of p. Plz answer this question ?.
If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided by (x -3) then the remainder in each case is same. Find value of p. Plz answer this question ? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided by (x -3) then the remainder in each case is same. Find value of p. Plz answer this question ? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If polynomial pxcube 4xsquare 3x - 4 and xcube - 4x p are divided by (x -3) then the remainder in each case is same. Find value of p. Plz answer this question ?.
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