Question

Find the value of k so that (x-1) is a factor
of the polynomial 5x3+4x² - 6x + 2k.
(2​

Answer 1

Answer:

Put x=1

we get

5(1)^3+4(1)^2-6(1)+2k=0

5+4-6+2k=0

k=-3/2

Step-by-step explanation:

Answer 2

Polynomial : 5x³ + 4x² - 6x + 2k.

Factor of Polynomial : (x - 1).

To Find : Value of k.

Solution :-

x ‐ 1 = 0.

x = 1.

Now, Substitute this value in the polynomial.

➙ 5x³ + 4x² - 6x + 2k = 0.

➙ 5(1)³ + 4(1)² - 6(1) + 2k = 0.

➙ 5 × 1 × 1 × 1 + 4 × 1 × 1 - 6 + 2k = 0.

➙ 5 + 4 - 6 + 2k = 0.

➙ 9 - 6 + 2k = 0.

➙ 3 + 2k = 0.

➙ 2k = -3.

➙ k = -3/2.

➙ k = -1.5

Verification :

➙ 5x³ + 4x² - 6x + 2k = 0.

➙ 5(1)³ + 4(1)² - 6(1) + 2(-1.5) = 0.

➙ 5 × 1 × 1 × 1 + 4 × 1 × 1 - 6 + -3 = 0.

➙ 5 + 4 - 6 - 3 = 0.

➙ 9 - 6 - 3 = 0.

➙ 3 - 3 = 0.

➙ 0 = 0.

LHS = RHS.

Hence, Verified.