Pg.15 Synthetic Division EQ: What is synthetic division and how is it used to determine roots and factors?

Dividend: the expression that is being divided Divisor: the expression you are dividing by Quotient: the solution after you divide Remainder: expression that is left over

Example) Divisor Quotient RemainderDividend

1. Find a root of the polynomial 2. Re-write the dividend so that no exponents are skipped 3. “Set up” using only the coefficients 4. Bring down the first value 5. Multiply, Add, Repeat 6.Degree drops by “1”

Ex 1) Divide by

Is 3 a factor of 12? YES!

Is 5 a factor of 12? NO!

The Remainder Theorem  P(a) = remainder when divided by (x – a)  If P(a) = 0, then “a” is a root.  If P(a) = 0 then (x – a) is a factor of P

Ex 2) Find P(-2) using the Remainder Theorem: (x+2) is not a factor

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If the polynomial crosses the x-axis at the value “a” then… 1.x = a is a root/zero 2.P(a) = 0 3.x – a is a factor of the polynomial 4.Dividing by x – 4 gives a remainder of 0