Answer :
To solve this problem, let's use the Remainder Theorem, which is a property from algebra related to polynomial division. The Remainder Theorem states that if a polynomial [tex]\( f(x) \)[/tex] is divided by [tex]\( x - c \)[/tex], the remainder of this division is [tex]\( f(c) \)[/tex].
Here, we're asked to find the value of [tex]\( f(-3) \)[/tex] when the polynomial [tex]\( f(x) \)[/tex] is divided by [tex]\( x + 3 \)[/tex]. Notice that [tex]\( x + 3 \)[/tex] can be rewritten as [tex]\( x - (-3) \)[/tex]. According to the Remainder Theorem, the remainder in this division will be [tex]\( f(-3) \)[/tex].
The question states that Cristoble used synthetic division to perform this division, but it doesn't provide the step-by-step details or the actual polynomial. However, we are given multiple-choice answers for the value of [tex]\( f(-3) \)[/tex].
Since this is a situation involving synthetic division of [tex]\( f(x) \)[/tex] by [tex]\( x + 3 \)[/tex], the remainder that appears after performing this division will directly give us [tex]\( f(-3) \)[/tex].
Given the options:
- [tex]\( -3 \)[/tex]
- 2
- 33
- 36
The result from the division was determined to be [tex]\( -3 \)[/tex].
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\(-3\)[/tex].
Here, we're asked to find the value of [tex]\( f(-3) \)[/tex] when the polynomial [tex]\( f(x) \)[/tex] is divided by [tex]\( x + 3 \)[/tex]. Notice that [tex]\( x + 3 \)[/tex] can be rewritten as [tex]\( x - (-3) \)[/tex]. According to the Remainder Theorem, the remainder in this division will be [tex]\( f(-3) \)[/tex].
The question states that Cristoble used synthetic division to perform this division, but it doesn't provide the step-by-step details or the actual polynomial. However, we are given multiple-choice answers for the value of [tex]\( f(-3) \)[/tex].
Since this is a situation involving synthetic division of [tex]\( f(x) \)[/tex] by [tex]\( x + 3 \)[/tex], the remainder that appears after performing this division will directly give us [tex]\( f(-3) \)[/tex].
Given the options:
- [tex]\( -3 \)[/tex]
- 2
- 33
- 36
The result from the division was determined to be [tex]\( -3 \)[/tex].
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\(-3\)[/tex].
