Question

factorise X ^ 4 + X ^ 3 - 7 x ^ 2 - x + 6​

Answer 1

→ x⁴ + x³ - 7x² - x + 6

This equation can be factorised using factor theorem.

When we x = 1, - 1, + 2 and - 3

→ p(1) = 1⁴ + 1³ - 7(1)² - 1 + 6

→ 0

→ p(-1) = 1 - 1 - 7(-1)² + 1 + 6

→ 0

→ p(-3) = 81 - 27 - 63 + 3 + 6

→ 0

→ p(2) = 16 + 8 - 28 - 2 + 6

→ 0

So factors are :-

(x - 1)(x + 2)(x + 3)(x - 2)