Decompose the polynomial into linear factors (x^2-7x+6)(x^2+3x-18)

Answer 1

To decompose the polynomial into linear factors, we first need to factor each quadratic polynomial individually.

1. Factor x^2-7x+6:
To factor this quadratic polynomial, we need to find two numbers that multiply to 6 and add up to -7. These numbers are -1 and -6.
So, we can rewrite the polynomial as (x-1)(x-6).

2. Factor x^2+3x-18:
To factor this quadratic polynomial, we need to find two numbers that multiply to -18 and add up to 3. These numbers are 6 and -3.
So, we can rewrite the polynomial as (x+6)(x-3).

Now, we can rewrite the original polynomial as the product of the linear factors:
(x^2-7x+6)(x^2+3x-18) = (x-1)(x-6)(x+6)(x-3)