When the polynomial P(x) = 3x^3 - kx^2 + 4x - 7 is divided by x - 2, the remainder is 9. W… — JAMB UTME

When the polynomial $P(x) = 3x^3 - kx^2 + 4x - 7$ is divided by $x - 2$ , the remainder is $9$ . What is the value of $k$ ?

Cevap: 4

The value of

k

4

According to the Remainder Theorem, dividing

P(x)

x - 2

leaves a remainder of

P(2)

. Evaluating

P(2) = 3(2)^3 - k(2)^2 + 4(2) - 7

gives

25 - 4k

. Setting

25 - 4k = 9

and solving yields

k = 4

Apply the Remainder Theorem

The remainder when

P(x)

is divided by

x - 2

P(2)

By the Remainder Theorem, dividing a polynomial

P(x)

x - a

leaves a remainder equal to

P(a)

Substitute

x = 2

into

P(x)

P(2) = 3(2)^3 - k(2)^2 + 4(2) - 7 = 25 - 4k

Evaluating the polynomial at

x = 2

expresses the remainder in terms of

k

Equate

P(2)

to the given remainder and solve for

k

25 - 4k = 9 \implies 4k = 16 \implies k = 4

Setting the calculated expression equal to

9

forms a linear equation that yields

k = 4

Polynomial Remainder Theorem

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