Please determine two different values of “b” in x^2 + bx + 30 so that the expression can be factored into the product of two binomials. Explain how you determined those values and show each factorization. Explain how your process would change if the expression was 2x^2 + bx + 30.

Question

Please determine two different values of “b” in x^2 + bx + 30 so that the expression can be factored into the product of two binomials.  Explain how you determined those values and show each factorization.  Explain how your process would change if the expression was 2x^2 + bx + 30.

ranga · Answer

I would make the discriminant a perfect square.  That way the expression can be nicely factored into the product of the form: (x + p)(x + q) where p and q are rational numbers.