Title: Academy Algebra II
1Academy Algebra II
- 5.5 Polynomial Long Division
- and Synthetic Division
- HW 5.4 p.357 (30-40 even, 46-54 even)
2Divide
3Polynomial Long Division vs. Synthetic Division
- Polynomial Long Division can be used for any two
polynomials. - Synthetic Division the divisor has to be in the
form x k, where k is any constant.
4Divide using polynomial long division
5Divide using synthetic division
6Divide
7Divide
8Divide
95.5 Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
10Academy Algebra II
- 5.5 FINISH Polynomial Long Division
- and Synthetic Division
- Hw 5.5 p.366 (8, 22, 28, 30, 32, 36)
11Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
- Steps
- 1.) Divide the polynomial and the factor.
- 2.) Factor the answer.
- 3.) Write out all factors.
12Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
13Given polynomial f(x) and a zero of f(x), find
the other zeros.
- Zeros answers to the polynomial equation f(x)
0. - Process.
- 1.) Use the zero to factor the polynomial
completely. - 2.) Solve to find the other zeros.
14Given polynomial f(x) and a zero of f(x), find
the other zeros.
15Given polynomial f(x) and a zero of f(x), find
the other zeros.
16Given polynomial f(x) and a factor of f(x),
factor f(x) completely.
17Given polynomial f(x) and a zero of f(x), find
the other zeros.
18Academy Algebra II
- 5.6 Find Rational Zeros
- HW tonight p.374 (4-10 even)
- Tomorrow p.374 (14-20 even)
- Next day p.374-375 (24-30 even)
19List all possible rational zeros using the
rational zero theorem.
- Every rational zero of a function has the
following form
20List all possible rational zeros using the
rational zero theorem.
- Example List the possible rational zeros for the
function
Factors of the constant Factors of
the leading coefficient
Possible rational zeros
Possible rational zeros
21List all possible rational zeros using the
rational zero theorem.
22List all possible rational zeros using the
rational zero theorem.
23Find the zeros of a polynomial function.
- List the possible rational zeros of the function.
- Test the zeros using division. (Since the zeros
are x-intercepts, when you divide you should end
up with a remainder of zero.) - Graph the function in the calculator to narrow
your list. Only check reasonable values from the
list. - The number of zeros is the same as the degree of
the polynomial.
24Find all real zeros of the function.
25Do Now Find all real zeros of the function.
26Academy Algebra II
- 5.6 Find Rational Zeros
- HW tonight p.374 (16-26 even)
- Quiz Friday 5.5, 5.6
- (Calculator and no calculator section)
27Find all real zeros of the function.
28Find all real zeros of the function.
29Do Now Find all real zeros of the function.