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Using Synthetic Division to Find The Zeros
Find all the zeros of f(x)=2x^3+ 1x^2– 38x + 35, using your calculator and synthetic division.
Fill in the steps below.
1. Put f(x)=2x + 1x2 – 38x + 35 into Yo on your calculator and hit Zoom 6.
2. By definition, the zero of a function is a number you put in to get ____
out.
Go to the TABLE (2nd graph) and find two ordered pairs with a y-value of 0.
They are
(___,0) and (__,0).
3. Having found two zeros, choose one of them and use synthetic division to divide and find the
quotient. Since we're dividing by a zero, the remainder had better be
Show work here:
Write the quotient out in full algebraic form (with the variable, not just the numbers):
______ This 1st quotient is a _____
(cubic, quadratic or linear).
4. Now take the 2nd zero, divide it into the 1st quotient (not the original polynomial).
Show work here:
Write the quotient out in full algebraic form (with the variable, not just the numbers):
____ This 2nd quotient is a _____
(cubic, quadratic or linear).
5. Set your 2nd quotient equal to 0 and solve it for the 3rd zero.
The three zeros are:____, ____
and _____
6. From the zeros write the factored form of f(x):
f(x) =(___)(____)(____)