Factor 5n^2+10n+20

Problem

5*n2+10*n+20

Solution

1. Identify the greatest common factor (GCF) of the terms 5*n2 10*n and 20

2. Determine that each coefficient is divisible by 5

3. Factor out the GCF of 5 from each term in the expression.

4. Divide each term by 5 to find the remaining polynomial inside the parentheses.

5. Check if the resulting quadratic n2+2*n+4 can be factored further using real numbers. Since the discriminant 2−4*(1)*(4)=−12 is negative, the quadratic is irreducible over the reals.

Final Answer

5*n2+10*n+20=5*(n2+2*n+4)

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