Question

What is the remainder when the polynomial f(x)=3x^3-4x^2+2x+8 is divided by (x-5)

Answer 1

The remainder when the polynomial f(x) = 3x³ - 4x² + 2x + 8 is divided by (x - 5) is constant an equal f(5).

Substitute x = 5 to the polynomial:

$f(5)=3(5^3)-4(5^2)+2(5)+8=3(125)-4(25)+10+8\\\\=375-100+18=275+18=293$

Answer: (3x³ - 4x² + 2x + 8) : (x - 5) = q(x) + 293.