Question

please help me to solve this question neatly.​

Answer 1

Required answer :

If (x + 1) is a factor of 3x² — 6x — k, then the value of k is 9.

Step-by-step explanation :

Given that, (x + 1) is a factor of 3x² — 6x — k, so :

➠ x + 1 = 0

➠ x = — 1

So, — 1 is the zero of the polynomial 3x² — 6x — k.

Now, let’s substitute x = — 1 and solve for k :

➠ 3x² — 6x — k = 0

➠ 3 (— 1)² — 6 (— 1) — k = 0

➠ 3 ( 1 ) + 6 — k = 0

➠ 3 + 6 — k = 0

➠ 9 — k = 0

➠ — k = — 9

➠ k = 9

Therefore, the value of k is 9 when (x + 1) is the factor of 3x² — 6x — k.

Verification :

Let’s substitute x = — 1 and k = 9 in the polynomial and verify :

➠ 3x² — 6x — k = 0

➠ 3 (— 1)² — 6 (— 1) — 9 = 0

➠ 3 ( 1 ) + 6 — 9 = 0

➠ 3 + 6 — 9 = 0

➠ 9 — 9 = 0

➠ 0 = 0

➠ LHS = RHS

➠ Hence, verified!

Answer 2

the value of k in the given question is 9