Question

28.Factorise x^(4)+x^(3)-7x^(2)-x+6 if it is given that x-2 is a factor of it.

topper can answer this step by step​

Answer 1

Answer:

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

Step-by-step explanation:

1^4 - 1^3 - 7*1^2 + 1 + 6 = 0.

So 1 is a root. We can factor out (x-1) to get

x^4 - x^3 - 7x^2 + x + 6 = (x-1)(x^3 - 7x - 6).

Always try x = -1.

(-1)^3 -7(-1) + 6 = 0.

So -1 is a root. Factor that out to get

(x-1)(x^3 - 7x - 6) = (x-1)(x+1)(x^2 - x - 6).

The last term is a quadratic that factors, so

x^4 - x^3 - 7x^2 + x + 6 =

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