Part 1 of 2 (a) Factor the polynomial over the set of real numbers. The factorization over the set of real numbers is \( x^{4}+5 x^{2}-14 \) \( f(x)= \)

To factor the polynomial \( x^{4}+5 x^{2}-14 \) over the set of real numbers, we can make a substitution. Let \( y = x^2 \). This transforms the polynomial into \( y^2 + 5y - 14 \). Next, we can factor this quadratic expression. We’re looking for two numbers that multiply to \(-14\) and add to \(5\). These numbers are \(7\) and \(-2\). Thus, we can express it as: \[ (y + 7)(y - 2) \] Now, substituting back \( y = x^2 \), we have: \[ (x^2 + 7)(x^2 - 2) \] This shows the complete factorization of the original polynomial over the set of real numbers: \[ f(x) = (x^2 + 7)(x^2 - 2) \] And there you have it, \( x^{4}+5 x^{2}-14 \) factored into real components!