let p be a polynomial p(x) = x^3+b*x^2+ c*x+24, where b and c are integers. Find a relation between b and c knowing that (x+2) divides p(x).

We know that (x+2) divides p(x), therefore p(x) can be written as p(x) = (x+2)q(x) + 0, where q is another polynomial of degree 2. We can calculate then p(-2): p(-2)= ((-2)+2)q(-2) = 0;p(-2)= (-2)^3+b(-2)^2+c(-2) +24=0, equivalent to p(-2)= -8+4b -2c +24=0, p(-2)= 4b-2c+16=0.Simplifying by dividing by 2: 2b-c+8=0.

Answered by Tina-Alina S. Maths tutor

3399 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

(x-4)^3


How can I maximise my performance and efficiency in an exam?


Find D when 8x^3-12x^2-2x+D is divided by 2x+1 when the remainder is -2


Solve the following simultaneous equations: 3x + 5y = -4 and -2x + 3y = 9


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences