1. Factorize each of the following expressions: \( \begin{array}{ll}\text { (a) } 12 x^{2}+9 x & \text { (b) } 20 x^{2}-4 x \\ \text { (c) }-20 x^{2}-15 x^{2} & \text { (d) }-6 x+4 x^{2}\end{array} \)

To factorize each of the given expressions, we will look for the greatest common factor (GCF) in each case. ### (a) \( 12x^2 + 9x \) 1. Identify the GCF of the coefficients (12 and 9), which is 3. 2. The variable part has \(x\) as a common factor. 3. Factor out the GCF: \[ 12x^2 + 9x = 3x(4x + 3) \] ### (b) \( 20x^2 - 4x \) 1. Identify the GCF of the coefficients (20 and 4), which is 4. 2. The variable part has \(x\) as a common factor. 3. Factor out the GCF: \[ 20x^2 - 4x = 4x(5x - 1) \] ### (c) \( -20x^2 - 15x^2 \) 1. Combine like terms first: \[ -20x^2 - 15x^2 = -35x^2 \] 2. The GCF here is \(-35x^2\) (since we can factor out the negative sign). 3. Factor out the GCF: \[ -35x^2 = -5x^2(7) \] ### (d) \( -6x + 4x^2 \) 1. Identify the GCF of the coefficients (-6 and 4), which is 2. 2. The variable part has \(x\) as a common factor. 3. Factor out the GCF, remembering to factor out the negative: \[ -6x + 4x^2 = 2x(2x - 3) \] ### Summary of Factorizations: - (a) \( 12x^2 + 9x = 3x(4x + 3) \) - (b) \( 20x^2 - 4x = 4x(5x - 1) \) - (c) \( -20x^2 - 15x^2 = -35x^2 \) - (d) \( -6x + 4x^2 = 2x(2x - 3) \)