Question

Let P and Q be the remainders when the polynomials x3 + 2x2

-5ax -7 and x3 +

ax2

-12x + 6 are divided by x+1 and x-2 respectively. If 2P + Q = 6, find the value

of a.​

Answer 1

Step-by-step explanation:

by remainder theorem

(x^3+2x^2-5ax-7)/(x+1)= -1+2+5a-7=5a-6=P

(x^3+ax^2-12x+6)/(x-2)= 8+4a-24+6=4a-10=Q

2P+Q=6

2(5a-6)+4a-10= 14a-22=6

14a=28

a=4