Let's solve the problem step-by-step to find the value of the given expression [tex]\(\frac{2b^2 + 4b - 9}{b + 4}\)[/tex] when [tex]\(b = -3\)[/tex].
1. Substitute [tex]\(b = -3\)[/tex] into the expression:
[tex]\[\frac{2(-3)^2 + 4(-3) - 9}{-3 + 4}\][/tex]
2. Calculate the components of the numerator:
- First, calculate [tex]\( (-3)^2 \)[/tex]:
[tex]\[ (-3)^2 = 9 \][/tex]
- Then, multiply this by 2:
[tex]\[ 2 \cdot 9 = 18 \][/tex]
- Next, calculate [tex]\( 4 \cdot (-3) \)[/tex]:
[tex]\[ 4 \cdot (-3) = -12 \][/tex]
- Now, combine these results with [tex]\(-9\)[/tex]:
[tex]\[ 18 + (-12) - 9 = 18 - 12 - 9 = 6 - 9 = -3 \][/tex]
3. Calculate the denominator:
[tex]\[ -3 + 4 = 1 \][/tex]
4. Divide the numerator by the denominator:
[tex]\[ \frac{-3}{1} = -3 \][/tex]
So, the value of the expression when [tex]\(b = -3\)[/tex] is [tex]\(-3\)[/tex].
Therefore, the correct answer is:
B. -3
