Factor 6x^2+78x+240

Problem

6*x2+78*x+240

Solution

1. Identify the greatest common factor by checking if all coefficients are divisible by the same number. Since 6 78 and 240 are all divisible by 6 factor out 6

6*(x2+13*x+40)

2. Find two numbers that multiply to the constant term 40 and add up to the linear coefficient 13

8×5=40

8+5=13

3. Factor the quadratic expression inside the parentheses using the numbers found in the previous step.

(x+8)*(x+5)

4. Combine the factors to write the final factored form of the original expression.

6*(x+8)*(x+5)

Final Answer

6*x2+78*x+240=6*(x+8)*(x+5)

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