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11. 1
Multiplying a Monomial by a Polynomial
NOTES
MULTIPLYING A MONOMIAL BY A POLYNOMIAL
monomial- no + or - signs
ex/ 5x2y3
b
inomial- ONLY 1 + or - sign
ex/ 5x3+3y
trinomial- ONLY 2 + and/or - signs
ex/ 7x2+6x+4
polynomial- 3 or more +/- signs
ex/ 5x2+y2+3x+2y-7
STEPS:
To distribute term outside ( ) to every term inside ( ) do the following:
1. Multiply the # outside ( ) by each # of each term inside ( )
2. Add the exponents of the variables in every term outside ( ) to the same variables in every
term inside ( )
3. Write your answer in standard form (put terms in order from highest to lowest
C
B
A
A
2a(a2-3a+1)
C
-3x3(2x4-x2-8)
B
1
4
x3(8x2+12x-4)
A
1
2
x2y(4x+2xy-8y)
A
BELLWORK
1. 3x (4x2 - 3x + 2)
2. -b4 (4b3 + b2 - 2b)
3. 12a2b (2ab2 + 1a - 3b)
11. 2
Multiplication of Binomials
(baby bear - c levels)
NOTES
MULTIPLICATION OF BINOMIALS
BOX MODEL:
(x+3)(2x-4)
F.O.I.L:
First Outer Inner Last
(2x-4)(x+3)
(x+3)(2x-4)
Examples:
C
C
C
Examples:
(2a-5)(a+4)
C
(x-8)(3x-4)
C
(2m2-6m)(m+2)
C
BELLWORK
11. 3
F.O.I.L.
(mama bear - b levels)
SQUARING
FOIL (Special Cases)
SQUARING BINOMIALS:
- When given a binomial squared, you must re-write to FOIL
ex/ (3x-2)2
ex/ (
4x+3)2
B
B
Plus/Minus:
- FOIL just like always :-) BUT - notice a patternBthat the middle term will cancel out
ex/ (x-2)(x+2)
ex/ (3a2+j)(3a2-j)
B
B
BELLWORK
11. 4
Multiplying Polynomials
(papa bear - a levels)
NOTES &
EX #1
Multiplying Polynomials
Each term from the first binomial should multiply to each term of the trinomial.
Ex1: (2x2-1)(4x2-3x+2)
A
Box
Method:
2
A
2
Ex2: (4x +5)(2x -5x+1)
Ex3: 3x4+(2x2-6)2
In HW
BELLWORK
11. 5
Factoring the Greatest Common Factor
Finding the GCF
FINDING THE GREATEST COMMON FACTOR
Finding the GCF:
1. 12, 6
2. 9x2, 15x
3. 30x4, 6x6, 18x2
4. x5y3, x8y2
5. 10a3b4c, 5ab3,
20a2b
Factoring a Polynomial:
C
1. 7x-14
C
2. 16x-8
B
3. 5x3+10x2-15x
B
4. 22x3+x5+14x7
5. 28x2y+14xy2-
7xy
A
BELLWORK
11. 6
Solving by Factoring Out the Greatest Common Factor
NOTES
& EX 1
Solving By Factoring Out the Greatest Common Factor
STEPS:
1. Set the equation equal to 0
2. Find the factors & GCF
3. Set each factor equal to 0 and solve
Ex1: 3x-6=0
C
C
B
A
Ex2: 2x+10=0
C
Ex3: 3x2-6x=0
B
Ex4: -4x2=12x
A
BELLWORK
11.8 7
11.
Factor
and
Solving
(Quadratics)
Factor
and
Solve Trinomials
Special Trinomials
NOTES
& EX 1
Factoring & Solving Trinomials (Quadratics)
STEPS:
1. Factor out the GCF if there is one
2. Factor the trinomial using factors of "c" that have a
"b"
3. Write as 2 binomials & FOIL to check answer
4. Set each binomial equal to 0 and solve.
Ex 1:
x2+9x+18
sum of
B,C
B,C
A
Ex 2:
x2+25x+24
B,C
Ex 3:
x2-11x+30
B,C
Ex 4:
5x2-30x+45
A
BELLWORK
11. 8
Factor and Solve Special Trinomials
B Levels
FOLDED PAPER INSERT
(C Levels)
STAPLE
C-Level Paper Examples
Factoring & Solve Special Trinomials
FACTOR & SOLVE: (B Level)
1. 25x -4=0
2. 16x2-81=0
3. 4x2-16=0
5. 9x2-81=0
2
A Level
The area of a rectangle is represented by x2-169
L
a) Write the expression for the length & width of the rectangle.
L =W
W=
b) If x=16 ft, what is L & W?
L=
W=
BELLWORK
11.9
Factor and Solve by Grouping
Ex 1
FOLDED PAPER INSERT
(Steps)
STAPLE
Steps:
(For polynomials with 4 terms, do not combine the like terms)
To Factor:
1.Look at the terms of the polynomial and see if
you can factor out a GCF.
2.Group the first two and last two terms of the
polynomial together.
3.Factor out the GCF separately for the terms
grouped together. (At this point you should
have 2 matching binomials.)
4.The remaining binomials should be the same.
If not, see if you can factor out a negative of
one of the groups to create common binomials.
5.The two GCFs come together to form a
binomial and the common binomial is the other
factor of the polynomial.
To Solve:
1. Set each binomial
equal to zero.
2. Solve each to find
the solutions
Factor & Solve by Grouping
1.
4x2+12x-x-3=0
2.
2x2+9x+5x+20=0
3.
9x2+36x-6x-24=0
BELLWORK
11.10
Quadratics with Leading Coefficients >1
Notes & Example
Quadratics with Leading Coefficients >1
Steps:
1. Multiply "a" times "c"
2. Find the factors of that product that add to "b"
3. Re-write trinomial as polynomial & follow steps from 11.9
1.
4x2+11x-3=0
B,C
A
2. 3x2+10x-8=0
B,C
3. 4x2+26x+40=0
A
BACK COVER SIDE
4. 18x2-20x-3=9x+12
BELLWORK