How do you use synthetic substitution to evaluate f(2) for #f(x)=x^4-4x^3+2x^2-3#?

1 Answer
Jul 9, 2015

Answer:

#f(2)=-11# (using synthetic substitution, below)

Explanation:

Rewrite #f(x)# so all powers of #x# are represented (in descending power sequence).
#color(white)("XXXX")##f(x)=x^4-4x^3+2x^2+0x-3#

#color(red)("[A]")##color(white)("XXXX")#Write the substitution value (#2#) separated by a vertical bar from a row of the from the coefficients as noted above.
#color(white)("XXXXXX")#Draw a vertical line below the coefficients, allowing enough space to write another row of numbers between the coefficients and the line.

#color(red)("[B]")##color(white)("XXXX")#Copy the first coefficient to a position below the line.

#color(red)("[C]")##color(white)("XXXX")#Multiply the substitution value and the number just written below the line and record the product above the line under the second coefficient.

#color(red)("[D]")##color(white)("XXXX")#Add the product just developed and the second coefficient and write the sum below the line.

#color(red)("[E]")##color(white)("XXXX")#Multiply the substitution value and the number just written below the line and record the product below the line.

#color(red)("[F] to [I]")##color(white)("XXXX")#Continue this process until all coefficients have been processed.

#color(red)("[I]")#The solution is the last value written below the line.

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