Question

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

Answer 1

-22

Explanation:

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

=-81 +63 -12+8

=-22

Answer 2

`-22` (using synthetic substitution)

Explanation:

Refer to the details below the diagram for an explanation of each step:

`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.