How do you use synthetic substitution to find x=3 for #f(x)=-3x^3+7x^2-4x+8#?

2 Answers
Sep 29, 2015

Answer:

-22

Explanation:

f(3) would be #-3(3)^3 +7(3)^2 -4(3) +8#

=-81 +63 -12+8

=-22

Sep 29, 2015

Answer:

#-22# (using synthetic substitution)

Explanation:

Refer to the details below the diagram for an explanation of each step:
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#color(red)("[1]")#
Write substitution value (in this case #3#) in a box to left side and the coefficients of the (canonically formed) polynomial to the right (in this case: #(-3x^3+7x^2-4x+8) rarr (-3 +7 -4 +8)#);
leave space for another line of numbers under this, then draw a vertical line.

#color(red)("[2]")#
Copy the first (highest order) coefficient to below the line.

#color(red)("[3]")#
Multiply the substitution value and the left-most value under the line and write the product under the second coefficient.

#color(red)("[4]")#
Add the two values in the second coefficient position and write the sum below the line.

#color(red)("[5]")#
Multiply the substitution value and the second value under the line and write the product under the third coefficient.

#color(red)("[6]")#
Add the two values in the third coefficient position and write the sum below the line.

#color(red)("[7]")#
Multiply the substitution value and the third value under the line and write the product under the fourth coefficient.

#color(red)("[8]")#
Add the two values in the fourth coefficient position and write the sum below the line.

This last sum is the value of the expression at the substitution value.