Question

Factorise x⁴ + x² + 1 with step by step explanation class 8th question....​

Answer 1

Answer: Let the number must be divided by x

Hence, the number must be divided by (7÷5).

Please refer to the attachment for explanation. Hope it helps.

Step-by-step explanation:

Consider x4 + x2 + 1

= (x4 + 2x2 + 1) – x2

= [(x2)2 + 2x2 + 1] – x2

= [x2 + 1]2 – x2

It is in the form of (a2 – b2) = (a + b)(a – b)

Hence [x2 + 1]2 – x2 = [x2 + 1 + x] [x2 + 1 – x]

Answer 2

⟶ x⁴ + x² + 1

⟶ x⁴ + x³ + x² - x³ - x² - x + x² + 1

⟶ x⁴ + x³ + 1x² - x³ - x² - x + x² + x + 1

⟶ (x² + x + 1) . x² - x³ - x² - x + x² + x + 1

⟶ (x² + x + 1) . x² - x³ - x² - x + 1 (x² + x + 1)

⟶ (x² + x + 1) . x² - (x³ + x² + x) + 1(x² + x + 1)

⟶ (x² + x + 1) x² - (x³ + x² + 1x) + 1(x² + x + 1)

⟶ (x² + x + 1) x² - (x² + x + 1) x + 1(x² + x + 1)

⟶ (x² + x + 1) x² + (x² + x + 1) + 1(x² + x + 1)

⟶ (x² + x + 1) x² + (x² + x + 1) (-x) + 1(x2 + x + 1) (x² - x + 1) (x² + x + 1)

⟶⟶ (x² - x + 1) (x² + x + 1) ✔