3X2 + 4X + 5
3
4X
– 7X
-3X
WARM UP: NAME THE ABOVE
POLYNOMIALS BASED ON DEGREE AND
NUMBER OF TERMS
TEST TOMORROW
26 Questions total
• 4 questions – put the following in standard
form and name based on degree and number
of terms
• 4 questions – Add or subtract the following
polynomials, put your answer in standard form
• 4 questions – multiply by distribution
TEST TOMORROW
• 4 questions – Multiply using F.O.I.L. or the the
box method ( make sure to combine like terms)
• 2 questions – Multiply the following polynomials
that are not binomials
• 6 questions – Multiply the following binomials
that are “Special cases”
• 2 Draw the multiplied result of the following
algebra tiles (complete the rectangle)
TEST TOMORROW
• 100 points total (4 points each)
• You can choose to leave one blank or work all of
the problems and I’ll just not count the problem
you do the worst on.
CLASSIFYING
POLYNOMIALS BY DEGREE
Polynomials
Classifying Polynomials by length
A polynomial with only one term is called a monomial.
A polynomial with two terms is called a binomial.
A polynomial with three terms is called a trinomial.
A polynomial with more than three terms is called a
polynomial with _______ terms
PUT THE FOLLOWING IN STANDARD
FORM AND NAME BASED ON
DEGREE AND NUMBER OF TERMS
2x – 5x + 3x2
4x2 + 3x3 – 4x + 6
PUT THE FOLLOWING IN STANDARD
FORM AND NAME BASED ON
DEGREE AND NUMBER OF TERMS
3x3 + 2x + 3x4
4x2 + 3x3 - 4x2
ADDING AND SUBTRACTING
POLYNOMIALS
• Don’t add the exponents
• Only combine if they have the
same variable(s) and the same
exponent
• Add or subtract the coefficients
only
ADD OR SUBTRACT THE
FOLLOWING POLYNOMIALS, PUT
YOUR ANSWER IN STANDARD FORM
(2x2 + 4x – 3) + (3x2 – 2x + 7)
(2x3 – 5x) + (3x3 + 2x2)
ADD OR SUBTRACT THE
FOLLOWING POLYNOMIALS, PUT
YOUR ANSWER IN STANDARD FORM
(3x2 - 5x + 2) - (3x2 + 2x - 3)
(4x3 – 5x) + (3x3 - 3x2 + 6)
Adding Polynomials
Add or subtract the following polynomials, put your
answer in standard form
(5x 3 – x + 2 x 2 + 7) + (3x 2 + 7 – 4 x) + (4x 2 – 8 – x 3)
SOLUTION
Adding Polynomials
Add or subtract the following polynomials, put your
answer in standard form
(2 x 2 + x – 5) + (x + x 2 + 6)
SOLUTION
Subtracting Polynomials
Add or subtract the following polynomials, put your answer
in standard form
(–2x 3 + 5x 2 – x + 8) – (–2x 3 + 3x – 4)
SOLUTION
No change
Subtracting Polynomials
Add or subtract the following polynomials, put your answer
in standard form
(–2x 3 + 5x 2 – x + 8) – (–2x 2 + 3x – 4)
SOLUTION
MULTIPLY BY DISTRIBUTION
Multiply the coefficients (numbers)
Add the exponents
MULTIPLY BY DISTRIBUTION
-y(4y2 + 2y – 3)
2x2 ( 3x2 – 4x + 6)
MULTIPLY BY DISTRIBUTION
3x2 (x3 + 4)
ab(a3 + 3ab2 – b3)
MULTIPLY BY DISTRIBUTION
-3X2Y3(Y2 – X2 + 2XY)
4X(3X2 – 2)
REMEMBER, FOIL REMINDS YOU TO
MULTIPLY THE:
First terms
Outer terms
Inner terms
Last terms
THE THIRD METHOD IS THE BOX
METHOD. THIS METHOD WORKS FOR
EVERY PROBLEM!
Here’s how you do it.
Multiply (3x – 5)(5x + 2)
Draw a box. Write a polynomial on the
top and side of a box. It does not
matter which goes where.
This will be modeled in the next
problem along with FOIL.
3x
5x
+2
-5
MULTIPLY USING F.O.I.L. OR THE
THE BOX METHOD ( MAKE SURE
TO COMBINE LIKE TERMS)
(x – 6)(x + 2)
(x + 4)(x – 7)
MULTIPLY USING F.O.I.L. OR THE
THE BOX METHOD ( MAKE SURE
TO COMBINE LIKE TERMS)
(2x – 6)(3x + 2)
(-2x + 4)(3x2 – 7)
MULTIPLY USING F.O.I.L. OR THE
THE BOX METHOD ( MAKE SURE
TO COMBINE LIKE TERMS)
(4x + 6) (3x2 – 5)
(2x – 5)(3x – 2)
MULTIPLY THE FOLLOWING
POLYNOMIALS THAT ARE NOT
BINOMIALS
(x + 3) ( x2 + 4x – 6)
MULTIPLY THE FOLLOWING
POLYNOMIALS THAT ARE NOT
BINOMIALS
(x + 2)(x2 + 4x – 3)
MULTIPLY THE FOLLOWING
POLYNOMIALS THAT ARE NOT
BINOMIALS
(x - 3)(1 + 3x – x2)
THERE ARE FORMULAS
(SHORTCUTS) THAT WORK FOR
CERTAIN POLYNOMIAL
MULTIPLICATION PROBLEMS.
2
B)
2
=A
2
B
(A +
+ 2AB +
2
2
2
(A - B) = A – 2AB + B
(A - B)(A + B) = A2 - B2
MULTIPLY THE FOLLOWING
BINOMIALS THAT ARE
“SPECIAL CASES”
(x +
2
4)
(3x +
2
2y)
MULTIPLY THE FOLLOWING
BINOMIALS THAT ARE
“SPECIAL CASES”
(x -
2
5)
(6x -
2
1)
MULTIPLY THE FOLLOWING
BINOMIALS THAT ARE
“SPECIAL CASES”
(x + 6)(x – 6)
(2x – 3)(2x + 3)
DRAW THE MULTIPLIED RESULT OF THE
FOLLOWING ALGEBRA TILES (COMPLETE
THE RECTANGLE)
Multiply (x + 2)(x + 1)
DRAW THE MULTIPLIED RESULT OF THE
FOLLOWING ALGEBRA TILES (COMPLETE
THE RECTANGLE)
Multiply (x - 1)(x - 3)