Date post: | 03-Jan-2016 |
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EXAMPLE
Divide using long division. State the quotient, q(x), and the remainder, r(x).
(6x³ +17x²+ 27x + 20) (3x + 4)
EXAMPLE
Divide using long division. State the quotient, q(x), and the remainder, r(x).
24 8 6 2 1x x x
REMAINDERS CAN BE USEFUL!
THE REMAINDER THEOREM: If the polynomial P(x) is divided by (x – a), then the remainder is P(a).
SYNTHETIC DIVISION Quick method of dividing polynomials
Used when the divisor is of the form x – a
Last column is always the remainder
FACTOR THEOREM For a polynomial P(x), x-a is a factor if an only if
P(a)=0
Or in other words, 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.
If we know a factor, we know a zero! If we know a zero, we know a factor!