Question

if th polynomial x^3 +2x^2-5ax-8 and x^3 +a^2-12x-6 when divided by x-2 and x-3 leave remainder p and q .if q-p =10 find a

Answer 1

Given x^3+2x^2-5ax-8 and x^3+ax^2-12x-6 when divided by x-2 and x-3 respectively then remainders are p and q
q-p=10
a=?
Let f(x)=x^3+2x^2-5ax-8
p (x)=x^3+ax^2-12x-6
By remainder theorem
f (2)=2^3+2×2^2-5a (2)-8
p=8+8-10a-8
p=8-10a
p (3)=3^3+a×3^2-12 (3)-6
q=27+9a-36-6
q=27-42+9a
q=-15+9a
Given q-p=10
-15+9a-8+10a=10
-23+19a=10
19a=10+23
19a=33
a=33/19

Answer 2

Answer:33/19

Step-by-step explanation: see in pic