If \( C=2 x^{2}+5 x-1 \) and \( D=x-1 \), find an expression that equals \( C-3 D \) in standard form. Answer Attempt 1 out of 2

To find the expression that equals \( C - 3D \), we first need to determine \( 3D \): \[ D = x - 1 \] Thus, \[ 3D = 3(x - 1) = 3x - 3 \] Now, we can substitute \( C \) and \( 3D \) into the expression: \[ C - 3D = (2x^2 + 5x - 1) - (3x - 3) \] Distributing the negative sign gives us: \[ C - 3D = 2x^2 + 5x - 1 - 3x + 3 \] Now, combine like terms: \[ C - 3D = 2x^2 + (5x - 3x) + (-1 + 3) \] \[ C - 3D = 2x^2 + 2x + 2 \] The expression in standard form is: \[ C - 3D = 2x^2 + 2x + 2 \] This can also be factored to highlight a common factor: \[ C - 3D = 2(x^2 + x + 1) \] So, the final result is \( 2(x^2 + x + 1) \) or simply \( 2x^2 + 2x + 2 \) depending on your preference!