Sept 21 A2M1L11­SB The special Role of Zero in Factoring
September 21, 2015
The Special Role of Zero in Factoring
Standard A­APR.B.3
The Special Role of Zero in Factoring
Standard A­APR.B.3
Do Now:
Find all of the solutions to the equation Sept 21 A2M1L11­SB The special Role of Zero in Factoring
September 21, 2015
Given any two polynomial functions and , the set of solutions to the equation can be found by solving , solving , and combining the solutions into one set. 1) Find the solution of: Sept 21 A2M1L11­SB The special Role of Zero in Factoring
September 21, 2015
Sept 21 A2M1L11­SB The special Role of Zero in Factoring
Find the zeros:
(x ­ 1)(2x + 1)(2x ­ 5) = 0
September 21, 2015
Sept 21 A2M1L11­SB The special Role of Zero in Factoring
September 21, 2015
p(x)= (x­2)(x+3)2
r(x)= (x­2)4(x+3)2
q(x)= (x­2)2(x+3)2
Zeros are ­3 and 2 for all 3 functions
Polynomial functions p(x)= (x­2)(x+3)2
Find the Zeros
2,­3
2,­3
q(x)= (x­2)2(x+3)4
2,­3
r(x)= (x­2)4(x+3)5
Even though these polynomial functions have the same zeros, they are not the same function; they do not even have the same degree! Sept 21 A2M1L11­SB The special Role of Zero in Factoring
September 21, 2015
p(x)= (x­2)(x+3)(x+3)
q(x)= (x­2)(x­2)(x+3)(x+3)(x+3)(x+3)
r(x)= (x­2)(x­2)(x­2)(x­2)(x+3)(x+3)(x+3)(x+3)(x+3)
Multiplicity is the count of the number of times a factor appears in a factored polynomial expression.
Find the zeros of the following polynomial functions, with their multiplicities. h(x)=(2x­3)5
with multiplicity
with multiplicity
g(x) = (x­4)3(x­2)8
Sept 21 A2M1L11­SB The special Role of Zero in Factoring
September 21, 2015
Find the zeros of the following polynomial functions, with their multiplicities. f(x) = (x+1)(x­1)(x2+1)
k(x) = (3x+4)100(x­17)4
a)Find a polynomial function that has the following zeros and multiplicities. b)What is the degree of your polynomial?
Zero
Multiplicity
Sept 21 A2M1L11­SB The special Role of Zero in Factoring
September 21, 2015
Find the zeros with multiplicity for the function: ( )=( 3−8)( 5−4 3). Can you find a rule that relates the multiplicities of the zeros to the degree of the polynomial function?
If p can be factored into linear terms, then the sum of the multiplicities of all of the zeros is exactly to the degree .
Sept 21 A2M1L11­SB The special Role of Zero in Factoring
September 21, 2015
Lesson Summary
Given any two polynomial functions p and q,
the solution set of the equation p(x)q(x)=0 can be quickly found by solving the two equations p(x)=0 and q(x)=0 and combining the solutions into one set.
The number a is zero of a polynomial function p with multiplicity mif the factored form p contains (x­a)
HW The special role of zero in factoring worksheet