Question

If the polynomials $2 x^3 + ax^2 + 4 x - 12$ and $x^3 + x^2 - 2 x + a$ leave the same remainder when divided by $(x - 3)$, find the value of $a$. Also find the remainder.

Answer 1

Put x = 3 in equation 1 we get Remainder = 2 * 3^3 + a * 3^2 + 4*3 -12 = 54 + 9a now put x= 3 in equation 2 we get remainder = 3^3+3^2 -2*3 + a = 30 +a now a/q remainders are equal we have 54+9a= a+31 => 8a=-54+30 =>a=-24/8 = -3 answer

Answer 2

x-3=0 => x=3

p(3)=2*3^3+a*3^2+4*3-12=
2*27+9a+12-12
54+9a

p(3)=3^3+3^2-2*3+a
27+9-6+a=
30+a

54+9a=30+a
54-30=a-9a
24=-8a
a=24:(-8)
a=-3