If (x - 1) is a factor of the polynomial P(x) = x^3 + 2x^2 - 5x + k, what is the value of … — JAMB UTME

If $(x - 1)$ is a factor of the polynomial $P(x) = x^3 + 2x^2 - 5x + k$ , what is the value of $k$ ?

Cevap: 2

The value of

k

2

According to the Factor Theorem, a linear polynomial

(x - a)

is a factor of

P(x)

if and only if

P(a) = 0

. For the factor

(x - 1)

, setting

x = 1

gives

P(1) = (1)^3 + 2(1)^2 - 5(1) + k = 0

. Simplifying yields

1 + 2 - 5 + k = 0

, which simplifies further to

-2 + k = 0

, giving

k = 2

Apply the Factor Theorem

P(1) = 0

Since

(x - 1)

is a factor, setting

x = 1

makes the polynomial equal to zero.

Substitute

x = 1

into

P(x)

1^3 + 2(1)^2 - 5(1) + k = 0

Evaluate the polynomial expression at

x = 1

Simplify and solve for

k

k = 2

Combine constants

1 + 2 - 5 = -2

and solve

-2 + k = 0

Factor Theorem

Soru