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What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3?
Most Upvoted Answer
What should be added to the polynomial x power3-3xpower2 6x-15 so that...
The remainder when f(x) is divided by (x-a)
is f(a)
Let f(x)= x³-3x² +6x-15
The remainder when f(x) is divided by (x-3)
=f(3)
=(3)³-3(3)² +6(3)-15
=27-27+18-15
=3
Therefore -3 should be added to the given polynomial so that it is exactly divisible by (x-3).
is f(a)
Let f(x)= x³-3x² +6x-15
The remainder when f(x) is divided by (x-3)
=f(3)
=(3)³-3(3)² +6(3)-15
=27-27+18-15
=3
Therefore -3 should be added to the given polynomial so that it is exactly divisible by (x-3).
Community Answer
What should be added to the polynomial x power3-3xpower2 6x-15 so that...
Solution:
Divisibility Rule:
If a polynomial P(x) is completely divisible by (x-a), then P(a) = 0.
Given Polynomial:
P(x) = x³ - 3x² + 6x - 15
Divisibility by x-3:
To check if P(x) is completely divisible by (x-3), we need to check whether P(3) = 0 or not.
P(3) = (3)³ - 3(3)² + 6(3) - 15
= 27 - 27 + 18 - 15
= 3
Since P(3) ≠ 0, P(x) is not completely divisible by (x-3).
Adding a Term:
To make P(x) completely divisible by (x-3), we need to add a term of the form (x-a) where a = 3.
Let Q(x) = P(x) + (x-3) = x³ - 3x² + 6x - 15 + x - 3
= x³ - 3x² + 7x - 18
Divisibility by x-3:
To check if Q(x) is completely divisible by (x-3), we need to check whether Q(3) = 0 or not.
Q(3) = (3)³ - 3(3)² + 7(3) - 18
= 27 - 27 + 21 - 18
= 3
Since Q(3) = 0, Q(x) is completely divisible by (x-3).
Therefore, the term (x-3) should be added to the polynomial x³ - 3x² + 6x - 15 to make it completely divisible by (x-3).
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What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3?
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What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3?.
What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3?.
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