Question

Write the expression x³+3x²+x-5 in terms of linear factors.

Answer 1

i (x - 1) (x^2 + 4 x + 5)

ii (x-1)(x + (2 - i)) (x + (2 + i))

Explanation:

To find the linear terms you have to factorize the polynomial.

Applying the difference of cubes, you find the first linear term. Using the quadratic formula you find the other linear terms.

`(-b - √(b^2 - 4ac))/(2a)`

`(-b + √(b^2 - 4ac))/(2a)`

As you may see the last terms are complex because the result of the square root is negative.

(x + (2 - i)) (x + (2 + i))