Factor x^2+3x-2

Problem

x2+3*x−2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=1 b=3 and c=−2

2. Check for integer factors by looking for two numbers that multiply to a*c=−2 and add to b=3 The factor pairs of −2 are (1,−2) and (−1,2) neither of which sum to 3

3. Apply the quadratic formula to find the roots of the equation x2+3*x−2=0 since it cannot be factored using integers.

x=(−b±√(,b2−4*a*c))/(2*a)

4. Substitute the values into the formula.

x=(−3±√(,3−4*(1)*(−2)))/(2*(1))

5. Simplify the expression under the radical.

x=(−3±√(,9+8))/2

x=(−3±√(,17))/2

6. Write the factors using the roots (r_1)=(−3+√(,17))/2 and (r_2)=(−3−√(,17))/2 in the form (x−(r_1))*(x−(r_2))

(x−(−3+√(,17))/2)*(x−(−3−√(,17))/2)

7. Simplify the signs within the factors.

(x+(3−√(,17))/2)*(x+(3+√(,17))/2)

Final Answer

x2+3*x−2=(x+(3−√(,17))/2)*(x+(3+√(,17))/2)

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