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Answer :
To find [tex]\( F(-5) \)[/tex] for the polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], follow these steps:
1. Substitute [tex]\(-5\)[/tex] into the polynomial for [tex]\( x \)[/tex]. This means you'll replace every [tex]\( x \)[/tex] in the expression with [tex]\(-5\)[/tex].
2. Calculate each part of the expression:
- First, compute [tex]\((-5)^2\)[/tex], which is the same as [tex]\(25\)[/tex].
- Next, compute [tex]\(-2 \times (-5)\)[/tex], which equals [tex]\(10\)[/tex].
- The constant term remains [tex]\(-7\)[/tex].
3. Combine these values by following the order of operations (PEMDAS/BODMAS):
- Start with the result from step 2: [tex]\(25\)[/tex].
- Add the result from multiplying [tex]\(-2\)[/tex] and [tex]\(-5\)[/tex] which is [tex]\(10\)[/tex]. So, [tex]\(25 + 10 = 35\)[/tex].
- Finally, subtract [tex]\(7\)[/tex]: [tex]\(35 - 7 = 28\)[/tex].
Therefore, [tex]\( F(-5) = 28 \)[/tex].
So, the correct answer is B. 28.
1. Substitute [tex]\(-5\)[/tex] into the polynomial for [tex]\( x \)[/tex]. This means you'll replace every [tex]\( x \)[/tex] in the expression with [tex]\(-5\)[/tex].
2. Calculate each part of the expression:
- First, compute [tex]\((-5)^2\)[/tex], which is the same as [tex]\(25\)[/tex].
- Next, compute [tex]\(-2 \times (-5)\)[/tex], which equals [tex]\(10\)[/tex].
- The constant term remains [tex]\(-7\)[/tex].
3. Combine these values by following the order of operations (PEMDAS/BODMAS):
- Start with the result from step 2: [tex]\(25\)[/tex].
- Add the result from multiplying [tex]\(-2\)[/tex] and [tex]\(-5\)[/tex] which is [tex]\(10\)[/tex]. So, [tex]\(25 + 10 = 35\)[/tex].
- Finally, subtract [tex]\(7\)[/tex]: [tex]\(35 - 7 = 28\)[/tex].
Therefore, [tex]\( F(-5) = 28 \)[/tex].
So, the correct answer is B. 28.
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