Factor 4x^2+21x+5

Problem

4*x2+21*x+5

Solution

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

2. Calculate the product of a and c which is 4×5=20

3. Find two numbers that multiply to 20 and add to the middle coefficient b=21 These numbers are 20 and 1

4. Rewrite the middle term 21*x using the two numbers found: 20*x+x

4*x2+20*x+x+5

5. Factor by grouping the first two terms and the last two terms.

4*x*(x+5)+1*(x+5)

6. Factor out the common binomial factor (x+5)

(4*x+1)*(x+5)

Final Answer

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

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