Factor 2x^2+6x-1

Problem

2*x2+6*x−1

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c Here, a=2 b=6 and c=−1

2. Check for factorability over the integers by calculating the discriminant D=b2−4*a*c

3. Calculate the discriminant: D=6−4*(2)*(−1)=36+8=44 Since 44 is not a perfect square, the expression cannot be factored using simple integer grouping.

4. Apply the quadratic formula x=(−b±√(,D))/(2*a) to find the roots for factoring over real numbers.

5. Solve for the roots: x=(−6±√(,44))/(2*(2))=(−6±2√(,11))/4=(−3±√(,11))/2

6. Write the factored form using the roots (r_1) and (r_2) as a*(x−(r_1))*(x−(r_2))

Final Answer

2*x2+6*x−1=2*(x−(−3+√(,11))/2)*(x−(−3−√(,11))/2)

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