Question

Find the value of k if the polynomial p(x) = 3x^3 + kx^2 + 5x - 16 is divided by (x-2) leaves a remainder-8

Answer 1

Answer :-

Using remainder theorem :-

→ x - 2 = 0

→ x = 2

Substituting the value of x = 2 and equating to - 8 :-

→ 3x³ + kx² + 5x - 16 = - 8

→ 3 ( 2 )³ + k ( 2 )² + 5 ( 2 ) - 16 = - 8

→ 3 × 8 + k × 4 + 10 - 16 = - 8

→ 24 + 4k - 6 = - 8

→ 4k - 18 = - 8

→ 4k = 18 - 8

→ 4k = 10

→ k = 10 / 4

→ k = 5 / 2

→ k = 2.5

Value of k = 2.5

Additional information :-

Polynomial :- An expression of the form p(x) = a₀ + a₁x + a₂x² + ... where a₀ , a₁ , a₂ are real numbers and x is variable is called polynomial in x.

Remainder theorem :- If a polynomial p(x) with degree greater than zero is divided by ( x - a ), then the remainder is equal to p(a).

Factor theorem :- Let p(x) be a polynomial. If p(a) = 0, then ( x - a ) is a factor of p(x).