We appreciate your visit to Cristoble used synthetic division to divide the polynomial tex f x tex by tex x 3 tex as shown in the table What is the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Certainly! To determine the value of [tex]\( f(-3) \)[/tex] when dividing a polynomial [tex]\( f(x) \)[/tex] by [tex]\( x+3 \)[/tex], we can use the Remainder Theorem. This theorem states that if a polynomial [tex]\( f(x) \)[/tex] is divided by [tex]\( x-c \)[/tex], the remainder of the division is [tex]\( f(c) \)[/tex].
Here's a step-by-step explanation:
1. Identify the divisor and the value to evaluate the polynomial at:
- The divisor is [tex]\( x+3 \)[/tex], which can be rewritten as [tex]\( x - (-3) \)[/tex].
- According to the Remainder Theorem, we will evaluate the polynomial at [tex]\( x = -3 \)[/tex].
2. Synthetic Division Insight:
- Synthetic division is a method used to divide polynomials when the divisor is of the form [tex]\( x-c \)[/tex].
- When you perform synthetic division with [tex]\( x+3 \)[/tex], you're essentially evaluating [tex]\( f(-3) \)[/tex].
3. Remainder Understanding:
- During synthetic division, the remainder is what you get after the division is complete, and this remainder is exactly the value of the polynomial evaluated at [tex]\( c \)[/tex]. In our case, [tex]\( f(-3) \)[/tex].
4. Result:
- Based on our understanding of synthetic division and the Remainder Theorem, the value of [tex]\( f(-3) \)[/tex] in this specific case is [tex]\( 2 \)[/tex].
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\( 2 \)[/tex].
Here's a step-by-step explanation:
1. Identify the divisor and the value to evaluate the polynomial at:
- The divisor is [tex]\( x+3 \)[/tex], which can be rewritten as [tex]\( x - (-3) \)[/tex].
- According to the Remainder Theorem, we will evaluate the polynomial at [tex]\( x = -3 \)[/tex].
2. Synthetic Division Insight:
- Synthetic division is a method used to divide polynomials when the divisor is of the form [tex]\( x-c \)[/tex].
- When you perform synthetic division with [tex]\( x+3 \)[/tex], you're essentially evaluating [tex]\( f(-3) \)[/tex].
3. Remainder Understanding:
- During synthetic division, the remainder is what you get after the division is complete, and this remainder is exactly the value of the polynomial evaluated at [tex]\( c \)[/tex]. In our case, [tex]\( f(-3) \)[/tex].
4. Result:
- Based on our understanding of synthetic division and the Remainder Theorem, the value of [tex]\( f(-3) \)[/tex] in this specific case is [tex]\( 2 \)[/tex].
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\( 2 \)[/tex].
Thanks for taking the time to read Cristoble used synthetic division to divide the polynomial tex f x tex by tex x 3 tex as shown in the table What is the. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
