5. Calculate the value of the expression \( 3 x^{2}+4 x-5 \) when \( \begin{array}{lll}\text { a) } x=-1 & \text { b) } x=-2 & \text { c) } x=0\end{array} \)

Sure, let's evaluate the expression \( 3x^{2} + 4x - 5 \) for each given value of \( x \). ## Expression: \[ 3x^{2} + 4x - 5 \] ## a) When \( x = -1 \): 1. **Substitute** \( x = -1 \) into the expression: \[ 3(-1)^{2} + 4(-1) - 5 \] 2. **Calculate the exponent**: \[ (-1)^{2} = 1 \] So, \[ 3(1) + 4(-1) - 5 \] 3. **Multiply**: \[ 3 \times 1 = 3 \] \[ 4 \times (-1) = -4 \] Now, \[ 3 - 4 - 5 \] 4. **Add/Subtract**: \[ 3 - 4 = -1 \] \[ -1 - 5 = -6 \] **Result**: \[ 3(-1)^{2} + 4(-1) - 5 = -6 \] --- ## b) When \( x = -2 \): 1. **Substitute** \( x = -2 \) into the expression: \[ 3(-2)^{2} + 4(-2) - 5 \] 2. **Calculate the exponent**: \[ (-2)^{2} = 4 \] So, \[ 3(4) + 4(-2) - 5 \] 3. **Multiply**: \[ 3 \times 4 = 12 \] \[ 4 \times (-2) = -8 \] Now, \[ 12 - 8 - 5 \] 4. **Add/Subtract**: \[ 12 - 8 = 4 \] \[ 4 - 5 = -1 \] **Result**: \[ 3(-2)^{2} + 4(-2) - 5 = -1 \] --- ## c) When \( x = 0 \): 1. **Substitute** \( x = 0 \) into the expression: \[ 3(0)^{2} + 4(0) - 5 \] 2. **Calculate the exponent**: \[ (0)^{2} = 0 \] So, \[ 3(0) + 4(0) - 5 \] 3. **Multiply**: \[ 3 \times 0 = 0 \] \[ 4 \times 0 = 0 \] Now, \[ 0 + 0 - 5 \] 4. **Add/Subtract**: \[ 0 + 0 = 0 \] \[ 0 - 5 = -5 \] **Result**: \[ 3(0)^{2} + 4(0) - 5 = -5 \] --- ## Summary of Results: - **a)** When \( x = -1 \), the expression evaluates to **-6**. - **b)** When \( x = -2 \), the expression evaluates to **-1**. - **c)** When \( x = 0 \), the expression evaluates to **-5**.