Using factor theorem, factorize the polynomial `x^4+x^3-7x^2-x+6`

Explanation

To factorize the polynomial \( P(x) = x^4 + x^3 - 7x^2 - x + 6 \) using the factor theorem, we will follow these steps:

### Step 1: Identify Possible Rational Roots
Using the Rational Root Theorem, we can test possible rational roots which are the factors of the constant term (6) divided by the factors of the leading coefficient (1). The possible rational roots are \( \pm 1, \pm 2, \pm 3, \pm 6 \).

### Step 2: Test \( x = 1 \)
We will substitute \( x = 1 \) into the polynomial:
\[
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