Understanding Polynomials
Adding Polynomials
Subtracting Polynomials
Multiplying Polynomials
Dividing Polynomials
100
Define a polynomial and give an example.
A mathematical expression made up of variables, coefficients, and exponents combined using addition, subtraction, and multiplication. For example:
3x² + 2x – 5.
100
Model the addition of x + 2 and 3x + 4 pictorially (with algebra tiles).
Shaded = negative
100
Model the difference of (5x - 3) - (2x + 4) pictorially (with algebra tiles).
100
Multiply (2x) by (3x + 4).
2x(3x+4) = 6x2+8x
100
What is 6x2 divided by 2x?
3x
200
What is the degree of the polynomial 3x2 + 5x - 4?
2
200
Explain a personal strategy for adding polynomials.
Answers will vary.
200
Subtract (x + 2) from (3x + 5).
(3x + 5)-(x + 2) = 2x +3
200
What is (x + 2)(3)?
3x+6
200
Find the quotient
x2-3x+9
300
Identify the coefficient(s) in the polynomial
2y2 + 3y + 1.
2 and 3
300
What do you get when you add 5a + 3b and 2a - 4b?
7a - b
300
What is the rule we follow when subtracting polynomials?
Add the opposite
300
What is a rule to explain how we multiply a monomial by a monomial?
Multiply the coefficients (numbers).
Add the exponents of like variables when the variables are the same.
300
Describe the steps for dividing a polynomial by a constant or monomial.
Separate the terms and divide them separately.
400
How many terms are in the polynomial 4x2 - x + 7? What is it called?
3 which is a trinomial
400
Explain how to use algebra tiles to add polynomials.
Large squares represent x2
Rectangles represent x
Small squares represent constants
400
Explain the error:
(4x2+3x−5)−(2x2+x+4)
=4x2+3x−5−2x2+x+4
=2x2+4x−1
It should be 3x + (-x) = 2x and (-5) + (-4) = -9. The correct answer is 2x2+2x-9.
400
Find the product of (3x)(−3x+1).
-9x2+3x
400
Find the error:
They should have done (-6x)/3 = -2x and 9/3 = 3
The correct quotient is 4x2-2x+3
500
What are the like terms in the polynomials:
4x - 2 and -7x + 5.
4x + (-7x) = -3x
(-2) + 5 = 3
500
Add x2 + 2x + 3 and 3x2 + 4x + 1.
4x2 + 6x +4
500
Simplify the expression (7x2+5x−3)−(3x2+2x-1).
4x2+3x-2
500
Find the product of 3x(2x2−4x+1).
6x3-12x2+3x
500
What is
2x2+3x-4