Factor x^2+5x+3

Problem

x2+5*x+3

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c Here, a=1 b=5 and c=3

2. Check for two integers that multiply to a*c=3 and add to b=5 The factors of 3 are 1 and 3 which sum to 4 No such integers exist.

3. Apply the quadratic formula to find the roots of the equation x2+5*x+3=0

x=(−b±√(,b2−4*a*c))/(2*a)

4. Substitute the values into the formula.

x=(−5±√(,5−4*(1)*(3)))/(2*(1))

5. Simplify the discriminant and the expression.

x=(−5±√(,25−12))/2

x=(−5±√(,13))/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+√(,13))/2

(r_2)=(−5−√(,13))/2

7. Construct the factored form.

x2+5*x+3=(x−(−5+√(,13))/2)*(x−(−5−√(,13))/2)

8. Simplify the signs within the factors.

x2+5*x+3=(x+(5−√(,13))/2)*(x+(5+√(,13))/2)

Final Answer

x2+5*x+3=(x+(5−√(,13))/2)*(x+(5+√(,13))/2)

Want more problems? Check here!