Factor completely \( 4 x^{2}+32 x-36 \)

To factor the expression \( 4x^{2} + 32x - 36 \), we can start by factoring out the greatest common factor (GCF) of the coefficients. The GCF here is 4: \( 4(x^{2} + 8x - 9) \) Next, we focus on the quadratic expression \( x^{2} + 8x - 9 \). We look for two numbers that multiply to -9 and add to 8. These numbers are 9 and -1. Therefore, we can factor the quadratic: \( 4(x + 9)(x - 1) \) So, the completely factored form of \( 4x^{2} + 32x - 36 \) is \( 4(x + 9)(x - 1) \).