use the grouping method to factor the polynomial below completely.
x^3+2x^2+3x+6
To factor the polynomial x^3 + 2x^2 + 3x + 6 completely using grouping, we will first group the terms in pairs:
x^3 + 2x^2 + 3x + 6
= (x^3 + 2x^2) + (3x + 6)
= x^2(x + 2) + 3(x + 2)
Now, we can factor out the common factor of (x + 2) from both sets of grouped terms:
= (x^2 + 3)(x + 2)
Therefore, the completely factored form of the polynomial x^3 + 2x^2 + 3x + 6 is (x^2 + 3)(x + 2).