Factor x^2+4x-3

Problem

x2+4*x−3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c Here, a=1 b=4 and c=−3

2. Check for two integers that multiply to a*c=−3 and add to b=4 The factors of −3 are (1,−3) and (−1,3) neither of which sum to 4

3. Apply the quadratic formula to find the roots of the equation x2+4*x−3=0 since it cannot be factored using integers.

x=(−b±√(,b2−4*a*c))/(2*a)

4. Substitute the values into the formula.

x=(−4±√(,4−4*(1)*(−3)))/(2*(1))

5. Simplify the expression under the radical.

x=(−4±√(,16+12))/2

x=(−4±√(,28))/2

6. Simplify the square root and the fraction.

x=(−4±2√(,7))/2

x=−2±√(,7)

7. Write the factors using the roots (r_1)=−2+√(,7) and (r_2)=−2−√(,7) in the form (x−(r_1))*(x−(r_2))

(x−(−2+√(,7)))*(x−(−2−√(,7)))

(x+2−√(,7))*(x+2+√(,7))

Final Answer

x2+4*x−3=(x+2−√(,7))*(x+2+√(,7))

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