Factor \( 20 b^{2}+15 b^{3} \) \( \square \)

To factor \( 20b^{2} + 15b^{3} \), first, identify the greatest common factor (GCF) of the coefficients and the variable terms. The GCF of 20 and 15 is 5, and the common variable factor is \( b^{2} \). So, you can factor out \( 5b^{2} \): \[ 5b^{2}(4 + 3b) \] And voilà! You've factored the expression to \( 5b^{2}(4 + 3b) \). Now, let’s see if you can find the zeros of the factored expression, which can be useful in different contexts like graphing or solving equations. Set \( 5b^{2}(4 + 3b) = 0 \) to find the values of \( b \) that satisfy the equation. You’ll find that \( b = 0 \) or \( b = -\frac{4}{3} \). Another way to understand factoring is to play around with different expressions. Take any polynomial, try to factor it systematically just like a puzzle! This playful practice will not only sharpen your skills but will also make factoring feel less daunting and more like a game.