Let's evaluate each expression step-by-step when [tex]\( x = -3 \)[/tex].
### Expression 39: [tex]\( 3x^2 - 6 \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex].
2. Compute [tex]\( (-3)^2 = 9 \)[/tex].
3. Multiply by 3: [tex]\( 3 \times 9 = 27 \)[/tex].
4. Subtract 6: [tex]\( 27 - 6 = 21 \)[/tex].
So, [tex]\( 3x^2 - 6 \)[/tex] evaluates to 21 when [tex]\( x = -3 \)[/tex].
### Expression 40: [tex]\( 2x^2 - 6x + 1 \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex].
2. Compute [tex]\( (-3)^2 = 9 \)[/tex].
3. Multiply by 2: [tex]\( 2 \times 9 = 18 \)[/tex].
4. Compute [tex]\( -6 \times (-3) = 18 \)[/tex].
5. Add these results along with 1: [tex]\( 18 + 18 + 1 = 37 \)[/tex].
So, [tex]\( 2x^2 - 6x + 1 \)[/tex] evaluates to 37 when [tex]\( x = -3 \)[/tex].
### Expression 41: [tex]\( -x^2 - 5x - 1 \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex].
2. Compute [tex]\( (-3)^2 = 9 \)[/tex].
3. Multiply by -1: [tex]\( -9 \)[/tex].
4. Compute [tex]\( -5 \times (-3) = 15 \)[/tex].
5. Add these results along with -1: [tex]\( -9 + 15 - 1 = 5 \)[/tex].
So, [tex]\( -x^2 - 5x - 1 \)[/tex] evaluates to 5 when [tex]\( x = -3 \)[/tex].
### Expression 42: [tex]\( x^2 + 3x + 8 \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex].
2. Compute [tex]\( (-3)^2 = 9 \)[/tex].
3. Compute [tex]\( 3 \times (-3) = -9 \)[/tex].
4. Add these results along with 8: [tex]\( 9 - 9 + 8 = 8 \)[/tex].
So, [tex]\( x^2 + 3x + 8 \)[/tex] evaluates to 8 when [tex]\( x = -3 \)[/tex].
### Expression 43: [tex]\( -2x^2 + 4x + 3 \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex].
2. Compute [tex]\( (-3)^2 = 9 \)[/tex].
3. Multiply by -2: [tex]\( -2 \times 9 = -18 \)[/tex].
4. Compute [tex]\( 4 \times (-3) = -12 \)[/tex].
5. Add these results along with 3: [tex]\( -18 - 12 + 3 = -27 \)[/tex].
So, [tex]\( -2x^2 + 4x + 3 \)[/tex] evaluates to -27 when [tex]\( x = -3 \)[/tex].
### Expression 44: [tex]\( -3x^2 - 6 - x \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex].
2. Compute [tex]\( (-3)^2 = 9 \)[/tex].
3. Multiply by -3: [tex]\( -3 \times 9 = -27 \)[/tex].
4. Subtract 6: [tex]\( -27 - 6 = -33 \)[/tex].
5. Add [tex]\( -x \)[/tex] which is [tex]\(-(-3) = 3 \)[/tex]: [tex]\( -33 + 3 = -30 \)[/tex].
So, [tex]\( -3x^2 - 6 - x \)[/tex] evaluates to -30 when [tex]\( x = -3 \)[/tex].
Therefore, the evaluated expressions are:
39. [tex]\( 3x^2 - 6 = 21 \)[/tex]
40. [tex]\( 2x^2 - 6x + 1 = 37 \)[/tex]
41. [tex]\( -x^2 - 5x - 1 = 5 \)[/tex]
42. [tex]\( x^2 + 3x + 8 = 8 \)[/tex]
43. [tex]\( -2x^2 + 4x + 3 = -27 \)[/tex]
44. [tex]\( -3x^2 - 6 - x = -30 \)[/tex]
