Class 10 Exam > Class 10 Questions > What should be added to the polynomial x powe...
Start Learning for Free
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).
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3?
Question Description
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?.
Solutions for What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? defined & explained in the simplest way possible. Besides giving the explanation of
What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3?, a detailed solution for What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? has been provided alongside types of What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? theory, EduRev gives you an
ample number of questions to practice What should be added to the polynomial x power3-3xpower2 6x-15 so that it completely divisible by x-3? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup