Answer :
Final answer:
To fully factor the expression 3x^3 + 45x^2 + 168x, we can factor out the greatest common factor 3x, leaving us with 3x(x^2 + 15x + 56). The quadratic expression can be factored into (x + 7)(x + 8). Therefore, the fully factored expression is 3x(x + 7)(x + 8).
Explanation:
To fully factor the expression 3x^3 + 45x^2 + 168x, we can first factor out the greatest common factor, which is 3x. This leaves us with 3x(x^2 + 15x + 56). Now we need to factor the quadratic expression x^2 + 15x + 56. We can find two numbers whose product is 56 and whose sum is 15. These numbers are 7 and 8. Therefore, the fully factored expression is 3x(x + 7)(x + 8).
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