Problem 195 - Elementary Algebra

Question

Factor. \(2 p^{2}+4 p+3\)

Step-by-Step Solution

Answer

Quadratic is not factorable over the real numbers.

Step 1: Identify the coefficients

Look at the quadratic equation and identify the coefficients. In this case, the quadratic is in the form of ax^2 + bx + c. Here, a = 2, b = 4, and c = 3.

Step 2: Calculate the discriminant

The discriminant in the quadratic formula is given by b^2 - 4ac. Substituting the values: b = 4, a = 2, and c = 3, we get: 4^2 - 4(2)(3)=16 - 24 = -8

Step 3: Conclusion

The quadratic equation 2p^2 + 4p + 3 has a discriminant less than zero indicating the roots are complex and not factorable over the real numbers.

Key Concepts

Coefficients in Quadratic Equations

To start solving a quadratic equation, you first need to identify its coefficients. A quadratic equation is typically written in the form of \( ax^2 + bx + c \). Each term in this equation has a coefficient:

• \