Factor 5x^2+21x+4

Problem

5*x2+21*x+4

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=5 b=21 and c=4

2. Find two numbers that multiply to a*c=5⋅4=20 and add to b=21

3. Determine the pair of numbers, which are 20 and 1 since 20⋅1=20 and 20 + 1 = 21$.

4. Rewrite the middle term 21*x using these two numbers as 20*x+1*x

5. Group the terms into two pairs: (5*x2+20*x)+(x+4)

6. Factor out the greatest common factor from each pair: 5*x*(x+4)+1*(x+4)

7. Factor out the common binomial (x+4) to obtain the final factored form.

Final Answer

5*x2+21*x+4=(5*x+1)*(x+4)

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