Terms you should know :
Example using long division:
The remainder is 15, the quotient is 25
Example of long division of polynomials :
This is your remainder.
Recall: Dividend = Quotient * Divisor + Reminder
Example 1:
a. Use long division to find the quotient and remainder if any.
b. Use Synthetic Division on the same problem.
Example 2:
Divide the fol lowing :
Example 3:
Divide the following:
Example 4:
Divide the following:
Here are two theorems that can be helpful in working with polynomials.
The Remainder Theorem: If P(x) is divided by x-c, then the remainder
is P(c).
The Factor Theorem : c is a zero of a P (x) if and only if x-c is a
factor of P(x), that is if the
remainder when dividing by x-c is zero.
You can use synthetic division and the remainder theorem to evaluate a
function at a given value .
Example 5: Use synthetic division and the remainder theorem to find
P(3) for
Example 6: Use synthetic division and the remainder theorem to find
P(-1) for
Example 7: Determine if x + 2 is a factor of
Example 8: Show that x = -1 is a zero of P(x) = 3x^3 - 15x^2 - 3x + 15
. Find the remaining
zeros of the function.
Example 9: Show that x =2 and x = -3 are zeros of P(x) = x^4 + 6x^3 +
3x^2 - 26x - 24.
Find the remaining zeros of the function.
Example 10: Find a 3rd degree polynomial with integer coefficients
given that 0, 2 and - 3 are
zeros.
