Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
57.9k views
in Mathematics by (35.7k points)

What must be added to x3 - 3x2 -12x +19 so that the result is exactly divisibly by x2 + x -6 ?

1 Answer

+1 vote
by (62.0k points)
selected by
 
Best answer

Let p(x) = x3 - 3x2 -12x +19 and q(x) = x2 + x -6.

By division algorithm, when p(x) is divided by q(x), the remainder is a linear expression in x

So, let r(x) = ax +b is added to p(x) so that p(x) + r(x) is divisible by q(x).

Hence, x3 - 3x2 -12x +19 is divisible by x2 + x -6 when 2x+5 is added to it.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...