Question

factorise x^3 -3x^2 +x+2. if x=√2+1​

Answer 1

Answer:

Step-by-step explanation:

(x³ - 3x² + x + 2) ÷ (x - 2) = x² - x - 1

x³ - 3x² + x + 2 = (x - 1)[x - (1 + √5)/2][x - (1 - √5)/2]

Answer 2

Answer:

(x-2)(x^2 - x - 2)

2 - √2

Step-by-step explanation:

Factorizing:

• x³ - 3x² + x + 2=
• x³ - 2x² - x² + 2x - x + 2 =
• x²(x-2) - x(x-2) - (x-2) =
• (x-2)(x^2 - x - 2)

Plug in the value of x:

• x= √2 + 1 ⇒ x² = (√2 + 1)² = 2+1+ 2√2 = 3+ 2√2

Finding the value:

• (x-2)(x^2 - x - 2) =
• (√2 +1 - 2) (3 + 2√2 - √2 - 1 -2) =
• (√2 -1)√2=
• 2 - √2