Factor 3x^2+5x+50

Problem

3*x2+5*x+50

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c Here, a=3 b=5 and c=50

2. Calculate the discriminant to determine if the quadratic can be factored over the set of rational numbers. The discriminant is given by D=b2−4*a*c

3. Substitute the values into the discriminant formula: D=5−4*(3)*(50)=25−600=−575

4. Analyze the result. Since the discriminant is negative (D<0, the quadratic has no real roots and cannot be factored into linear factors with real coefficients.

5. Conclude that the expression is irreducible over the field of real numbers.

Final Answer

3*x2+5*x+50=irreducible

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