Question

answer it with explanations​

Answer 1

Answer:

(x + 1) is not a factor of x³ - x² - (2 + $\sf{\sqrt{2}}$)x + $\sf{\sqrt{2}}$

Step-by-step explanation:

Given :

Polynomial = x³ - x² - (2 + $\sf{\sqrt{2}}$)x + $\sf{\sqrt{2}}$

Find the zeros of (x + 1) -

⇒ x + 1 = 0

⇒ x = –1

Substitute it → f(x)

⇒ f(–1) = (–1)³ – (–1)² – (2 + $\sf{\sqrt{2}}$)(–1) + $\sf{\sqrt{2}}$

⇒ –1 – (1) – (–2 – $\sf{\sqrt{2}}$)(–1) + $\sf{\sqrt{2}}$

⇒ –2 + 2 + $\sf{\sqrt{2}}$ + $\sf{\sqrt{2}}$

⇒ $\sf{\sqrt{2}}$ + $\sf{\sqrt{2}}$

⇒ 2$\sf{\sqrt{2}}$

2$\sf{\sqrt{2}}$ ≠ 0

Therefore, (x + 1) is not a factor of x³ - x² - (2 + $\sf{\sqrt{2}}$)x + $\sf{\sqrt{2}}$