Let f(x)=x^4-3x^3+5x use synthetic substitution to find f(-2)

Step-by-step explanation:

The Remainder Theorem states that when we divide a polynomial f(x)

by x − a the remainder R equals f(a).

a = -2

Syntetic substitution.

1. Write only the coefficients of x in the dividend inside an upside-down division symbol.

2. Put the divisor at the left.

3. Drop the first coefficient of the dividend below the division symbol.

4. Multiply the drop-down by the divisor, and put the result in the next column.

5. Add down the column.

6. Repeat 4 and 5 until you can go no farther

The remainder is 30, so f(-2) = 30.

Check:

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction