Question

Find the value of k if (x – 2) is a factor of 2x³ – 6x² + 5x + k. Also find whether x – 1 is a factor or not.

Answer 1

Step 1: Find the value of k using the Factor Theorem

If (x − 2) is a factor of the polynomial p(x) then p(2) = 0.

We substitute x = 2 into the polynomial p(x)

p(2) = 0

⇒ 2(2)³ – 6(2)² + 5(2) + k = 0

⇒ 2(8) – 6(4) + 10 + k = 0

⇒ 16 – 24 + 10 + k = 0

⇒ 2 + k = 0

∴ k = –2

Step 2: Determine if x – 1 is a factor

Substitute x = 1 into the polynomial

p(1) = 2(1)³ – 6(1)² + 5(1) – 2

= 2 – 6 + 5 – 2

= –1

Since p(1) ≠ 0

∴ (x – 1) is not a factor of the polynomial.