Algebra 2: Section 6-2 Polynomials and Linear Factors
Standard: Students graph quadratic functions and determine the minima, maxima,
and zeros of the function.
Factor Theorem
The expression x – a is a linear factor of a polynomial if and only if the value
a is a zero of the related polynomial function.
1.
2.
3.
4.
Equivalent Statements about Polynomials
– 4 is a solution of x 2  3x  4  0
– 4 is an x-intercept of the graph y  x 2  3x  4
– 4 is a zero of y  x 2  3x  4
x + 4 is a factor of x 2  3 x  4
Relative
minimum
value of y
Relative maximum
value of y
x-intercepts: values of x
for which y = 0
 A relative maximum is: the greatest y-value of the points in a region
of the graph.
 A relative minimum is: the least y-value among nearby points in the
graph.
 A multiple zero is: a zero that is repeated.
 The multiplicity of a zero of a polynomial function is: the number
of times the related linear factor is repeated in the factored form of
the polynomial.
Quick Check
Ex. 1) Write the expression ( x  1)( x  1)( x  2) as a polynomial in
standard form.
Ex. 2) Write the polynomial in factored form.
a) 3x 3  3x 2  36 x
b) 3x 3  9 x
Ex. 3)
a) Find all the zeros of the function.
y  ( x  5)( x  3)
(Change)
b) Graph the function and
label the zeros.
Day 2
Ex. 4)
a) Write a polynomial function in standard form with zeros at
- 4, - 2, and 1.
b) Write a polynomial function in standard form with zeros at
- 4, - 2, and 0.
c) Explain why the zero at 0 produces more than one possible answer to
part (b).
Day 1 Assignment page 323 #1-11 all, #16, 17
Day 2 #21-35 odds #41-45 all