Factor 3x^2-4x-8

Problem

3*x2−4*x−8

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c Here, a=3 b=−4 and c=−8

2. Calculate the product a*c which is 3×(−8)=−24

3. Search for two integers that multiply to −24 and add to b=−4 The pairs of factors for −24 are (1,−24) (−1,24) (2,−12) (−2,12) (3,−8) (−3,8) and (4,−6) (−4,6)

4. Determine if any pair sums to −4 The sums are −23,23,−10,10,−5,5,−2,2 None of these integer pairs sum to −4

5. Check the discriminant D=b2−4*a*c to see if the expression can be factored over the rational numbers.

D=(−4)2−4*(3)*(−8)

D=16+96

D=112

6. Conclude that since 112 is not a perfect square, the quadratic cannot be factored into binomials with rational coefficients. It is considered irreducible over the integers.

Final Answer

3*x2−4*x−8=3*x2−4*x−8

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