Factor x^2+5x+2

Problem

x2+5*x+2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=5 and c=2

2. Check for two integers that multiply to a*c=2 and add to b=5 The only integer factors of 2 are 1 and 2 which sum to 3

3. Apply the quadratic formula to find the roots, since the expression cannot be factored using integers.

x=(−b±√(,b2−4*a*c))/(2*a)

4. Substitute the values into the formula.

x=(−5±√(,5−4*(1)*(2)))/(2*(1))

5. Simplify the discriminant and the expression.

x=(−5±√(,25−8))/2

x=(−5±√(,17))/2

6. Write the factors using the roots (r_1) and (r_2) in the form (x−(r_1))*(x−(r_2))

(r_1)=(−5+√(,17))/2

(r_2)=(−5−√(,17))/2

Final Answer

x2+5*x+2=(x−(−5+√(,17))/2)*(x−(−5−√(,17))/2)

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