Question

if the polynomial p x cube + 4 x square + 3 x - 4 and x cube - 4 x + p are divided by x - 3 then the remainder in each case is same find the value of p​

Answer 1

Step-by-step explanation:

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