How to proof the remainder theorem …
CBSE, JEE, NEET, CUET
Question Bank, Mock Tests, Exam Papers
NCERT Solutions, Sample Papers, Notes, Videos
Posted by Radhika Singh 5 years, 3 months ago
- 2 answers
Gaurav Seth 5 years, 3 months ago
Remainder Theorem Proof
Theorem functions on an actual case that a polynomial is comprehensively dividable, at least one time by its factor in order to get a smaller polynomial and ‘a’ remainder of zero. This acts as one of the simplest ways to determine whether the value ‘a’ is a root of the polynomial P(x).
That is when we divide p(x) by x-a we obtain
p(x) = (x-a)·q(x) + r(x),
as we know that Dividend = (Divisor × Quotient) + Remainder
But if r(x) is simply the constant r (remember when we divide by (x-a) the remainder is a constant)…. so we obtain the following solution, i.e
p(x) = (x-a)·q(x) + r
Observe what happens when we have x equal to a:
p(a) = (a-a)·q(a) + r
p(a) = (0)·q(a) + r
p(a) = r
Hence, proved.
Test
Related Questions
Posted by Sheikh Alfaz 3 months, 1 week ago
- 0 answers
Posted by Duruvan Sivan 7 months, 3 weeks ago
- 0 answers
Posted by Akhilesh Patidar 1 year, 6 months ago
- 0 answers
Posted by Yash Pandey 7 months, 3 weeks ago
- 0 answers
Posted by Alvin Thomas 4 months, 2 weeks ago
- 0 answers
Posted by Savitha Savitha 1 year, 6 months ago
- 0 answers
myCBSEguide
Trusted by 1 Crore+ Students
Test Generator
Create papers online. It's FREE.
CUET Mock Tests
75,000+ questions to practice only on myCBSEguide app
Iqbal Hussain 5 years, 3 months ago
0Thank You