one less than the degree of the first term of
the dividend. The final value in the row is the
remainder.
Synthetic Division
Slide 8
Use synthetic division to divide 5x3 + 6x + 8 by x + 2.
Slide 9
Solution We begin the synthetic division process by bringing down 5. This is following by a series of multiplications and additions.
Text Example cont.
Slide 10
Text Example cont.
Slide 11
If the polynomial f (x) is divided by x c, then the remainder is f (c).
Slide 12
Let f (x) be a polynomial.
If f (c ) = 0, then x c is a factor of f (x).
If x c is a factor of f (x), then f ( c) = 0.
Slide 13
Text Example
Solve the equation 2x3 3x2 11x + 6 = 0 given that 3 is a zero of f (x) = 2x3 3x2 11x + 6.
Slide 14
Solution
Now we can solve the polynomial equation.
The solution set is {-2, 1/2 , 3}.
Text Example cont.