Question 87917: X^3 – 5x^2 + 2x + 20 divided by (x-3) gives a remainder of??
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! You can do this the obvious way, by dividing the x-3 into the polynomial. There are two ways to do this: long division and synthetic division.
However, you can also do this by substitution.
If P(x) = X^3 – 5x^2 + 2x + 20, then the remainder after division by x-3 is P(3).
P(3) = 3^3 -5*3^2 + 2*3 + 20
P(3) = 27 - 45 + 6 + 20
P(3)= 8
The remainder is 8.
You can also check this with a graphing calculator. You can graph the function y1=X^3 – 5x^2 + 2x + 20, and evaluate the function at x = 3. With a TI 83, 84, or 86, after you graph the function, you can look in the TABLE and look for x= 3. Or you can just hit the TRACE button, and type the number 3. The calculator gives the x and y value. The y value is the answer to the problem.
R^2 Retired from SCC
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