What is the remainder when the polynomial P(x) = x^3 + 3x^2 - 2x + 4 is divided by x - 1? — JAMB UTME

What is the remainder when the polynomial $P(x) = x^3 + 3x^2 - 2x + 4$ is divided by $x - 1$ ?

The remainder when

P(x)

is divided by

x - 1

6

According to the Remainder Theorem, dividing a polynomial

P(x)

by a linear divisor

x - a

leaves a remainder equal to

P(a)

. For the divisor

x - 1

, setting

x - 1 = 0

yields

x = 1

. Substituting

x = 1

into

P(x) = x^3 + 3x^2 - 2x + 4

gives

1 + 3 - 2 + 4 = 6

. Therefore, the value

6

is the correct remainder.

Apply the Remainder Theorem

To find the remainder when

P(x)

is divided by

x - a

, set

x - 1 = 0

, giving

x = 1

. The remainder is equal to

P(1)

By the Remainder Theorem, dividing a polynomial

P(x)

(x - a)

yields a remainder of

P(a)

Substitute

x = 1

into

P(x) = x^3 + 3x^2 - 2x + 4

P(1) = (1)^3 + 3(1)^2 - 2(1) + 4 = 1 + 3 - 2 + 4 = 6

Direct evaluation of the expression at

x = 1

yields the numerical value of the remainder.

The Remainder Theorem states that when a polynomial

P(x)

is divided by a linear factor

(x - a)

, the remainder is

P(a)

Question