3.5 Day 2 Solving Polynomials.notebook
3-5 Day 2 Solving Polynomials
I can...
November 16, 2015
Reminder Theorem: When dividing polynomials if you get a
remainder of 0, then the polynomial you
divided by is a factor of the original
polynomial
5x4 + 16x3 - 15x2 + 8x + 16 ÷ (x + 4)
Solve polynomials using factoring and
synthetic division
-4 5 16 -15 8 16
-20 16 -4 -16
5 -4 1 4 0
This means that (x + 4) is a factor of, 5x4 + 16x3 - 15x2 + 8x + 16.
Which means x = -4 is a solution.
Jun 17-7:50 AM
Jun 17-7:50 AM
Why do we need to know this?
Solve by factoring:
3
x - 9x2 + 27x + 27 = 0
**Stuck? Grouping doesn't work?
What if you knew that (x - 3) was
one factor?
How to solve using the remainder theorem:
1. Divide the polynomial by the given factor.
2. If the remainder is 0, then you have found one of the factors.
3. Write your result as a polynomial.
4. Factor that polynomial, and set all factors equal to zero.
Jun 17-7:50 AM
Jun 17-7:50 AM
Let's go back to this. Solve the polynomial
given that one of it's factors is (x - 3).
Example 1:
a) Is (x + 3) a factor of 2x3 – 3x2 – 17x + 30?
x3 - 9x2 + 27x - 27 = 0
3 1 -9 27 -27
3 -18 27
1 -6 9 0
Factor
b) Find all remaining factors.
x2 - 6x + 9
(x - 3)(x - 3)
c) Find all solutions/roots/zeros.
Take ALL factors and put them equal to zero.
(x - 3)(x - 3)(x - 3) = 0
x-3=0
Don't forget one of the
factors was given to you.
x-3=0 x-3=0
x = 3, 3, 3 or x = 3 (with a multiplicity of 3)
Jun 17-7:50 AM
Jun 17-7:50 AM
1
3.5 Day 2 Solving Polynomials.notebook
November 16, 2015
Example 2:
Example 3:
a) Is (x - 5) a factor of x3 – 7x2 +7x + 15?
a) Is (x - 2) a factor of x3 – 7x2 +4x + 12?
b) Find all remaining factors.
b) Find all remaining factors.
c) Find all solutions/roots/zeros.
c) Find all solutions/roots/zeros.
Jun 17-7:50 AM
Jun 17-7:50 AM
2