Question

using reminder theorem find the remainder when x cube minus 2 x square - 4 x minus 1 is divided by X + 1​

Answer 1

Answer:

given p(x) = x^3 - 2x^2 - 4x - 1 g(x) = x + 1

to find the remainder when p(x) is divided by g(x)

equate g(x) = x + 1 = 0, x = -1

therefore remainder r(x) = p(-1)

replace x in the polynomial by -1 and simplify to get the remainder. if the remainder is 0, then we say g(x) = x + 1 is a factor of the given polynomial p(x)

now, p(-1) = (-1)^3 - 2(-1)^2 - 4(-1) - 1

= -1 - 2(1) + 4 - 1

= -1 - 2 + 4 - 1

= -4 + 4

= 0

therefore remainder is 0 hence x + 1 is a factor of the given polynomial.