Question

find the remainder when f(x) is divided by (x-k)

f(x)=4x^3- 5x^2+2x+11 ; k=3

Answer 1

either divide using synthetic division, or find \(f(3)\)

Answer 2

damn latex is still out, ok find f(3)

Answer 3

so just plug in 3 wherever x is?

Answer 4

exactly.

Answer 5

might even use synthetic substitution to make it faster.

write down the value you are substituting, a vertical bar, and then the coefficients (in descending order of x^, with 0 in place of any missing terms):

3 | 4 -5 2 11

----------------
4

you also drop the first coefficient down below the line. now, repeat this process until you run out of numbers: multiply the substitution number on the left by the most recent number below the line (3*4) and write the result (12) above the line in the next column. add the numbers in that column and write the result below the line.

when you have used up all of the numbers, the last number on the right below the line is the value of that polynomial with the substitution number as its argument.

3 | 4 -5 2 11
12 21 69
----------------
4 7 23 80