Question

factor.\
$49w^2 + 69w + 25$

Explanation:

Step1: Check discriminant value

Calculate discriminant $\Delta = b^2-4ac$ for $ax^2+bx+c$.
$\Delta = 69^2 - 4\times49\times25$
$\Delta = 4761 - 4900 = -139$

Step2: Analyze discriminant result

Since $\Delta < 0$, the quadratic has no real roots, so it cannot be factored into linear terms with real coefficients. In the real number system, the expression remains in its original form.

Answer:

$49w^2 + 69w + 25$ (cannot be factored over the real numbers)