Bellwork
1. Find the product. Write in standard
form. 2x(x+2)(x-3)
2. Factor completely: 4x³ -24x²+32x
3. Factor completely:
4. Factor completely:
5. Factor completely: 8x³ +12x² -8x
6. Divide by HAND: 12,356÷3
Lesson7 .3
Products and Factors of Polynomials
DAY 2
Objectives:
 Day 1
 Multiply polynomials.
 Factor polynomials.
 Day 2
 Use substitution to determine factors of a function.
 Divide by using long division.
 Day 3
 Divide by using synthetic division.
Find the zeros of the function:
1.) What are the zeros
of the function?
2.) Now, write the
factors of the function!
Practice #2:
1.) Find the zeros
2.) Write the factors of the function
Practice #2:
Find the zeros, write the factors, and then write the
equation of the function.
The Factor Theorem states the relationship between the
linear factors of a polynomial expression and the zeros of
the related polynomial.
FACTOR Ex
THEOREM
x-r is a factor of the polynomial expression that defines the
function P if and only if r is a solution of P(x) =0, that is if and
only if P(r)=0.
EXAMPLE: Use substitution to determine whether x+2
is a factor of : x³ - 2x² - 5x + 6.
Practice: Use substitution to determine whether the
given linear expression is a factor of the polynomial.
 #1)x² +x +1; x-1
 Answer NO
 #2) x³ + 3x²-18x-40; x-4
 Answer YES
 #3) x² + 2x +1; x+2
 Answer NO
DIVIDING POLYNOMIALS
Example 1: x³+ 3x² -4x -12 divided by x-2
Example 2: x³+ 3x² +3x +2 divided by x² +x +1
DIVIDING POLYNOMIALS
*remainders*
Example 1: 8x³+ 12x² +6x +5 divided by 2x+1
Example 2: 6x² + 2x -5 divided by 3x + 5
Lesson7.3
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