Question

if the polynomial ax³+4x²+3x and x³+4x+a leave the same remainder when divided by (x-3) then find value of a

please only answer the questions​

Answer 1

Answer:

put x=3 in both polynomial

a*3^3+4*3^2+3*3=3^3+4*3+a

27a+36+9=27+12+a

26a=39-45

26a=-6

a=-6/26=-3/13

Answer 2

Answer:

Let p(x) = ax3 + 4x2 + 3x – 4 and q(x) = x3 – 4x + a be the given polynomials.

When p(x) and q(x) are divided by (x – 3) the remainder are p(3) and q(3) respectively.

p(3) = q(3) given

a(3)3 + 4(3)2 + 3 × 3 – 4 = 33 – 4 × 3 + a

⇒ 27a + 36 + 9 – 4 = 27 – 12 + a

⇒ 26a = 15 – 41

⇒ 26a = - 26

∴ a = - 26/26 = - 1