Questions: Factor the trinomial completely. 3m^2 + 10m + 21

Factor the trinomial completely. 3m^2 + 10m + 21
Transcript text: Factor the trinomial completely. \[ 3 m^{2}+10 m+21 \]
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Polynomial

We start with the trinomial \( 3m^{2} + 10m + 21 \).

Step 2: Attempt to Factor the Polynomial

We check if the polynomial can be factored into the form \( (am + b)(cm + d) \).

Step 3: Analyze the Factorization

After attempting to factor, we find that the polynomial does not factor into simpler integer polynomials. The expression remains as \( 3m^{2} + 10m + 21 \).

Step 4: Conclusion on Factorization

Since the polynomial cannot be factored further, we conclude that it is prime. Thus, the polynomial \( 3m^{2} + 10m + 21 \) does not have a factorization over the integers.

Final Answer

The polynomial is prime.

Was this solution helpful?
failed
Unhelpful
failed
Helpful