Investigate Polynomials

[corevet1]

1. Create two trinomials that you can add together to get 4x - 8. Explain how it is possible to combine (add) two trinomials and end up with a binomial answer.


2. Explain why the degree of the term
x +4⁵ is not 5. What is the degree?
3. Can the sum of two polygons in x, both of degree 4, be of degree 3? If so give an example.
4. Choose one or more of the following descriptions for each expressions. (a) polynomial, (b) polynomial written in descending order, (c) not a polynomial.
i) -6w³+ 7w² + 2w -11
ii) x⁵ + x⁹
iii) 4y³ - 3y + 2/y
iv) 3a⁵ -2a³ - 6a^-1 + 15
v) j^-1
vi) k⁶ - k⁴ + 3k - 2

 

[pka]

1. Create two trinomials that you can add together to get 4x - 8. Explain how it is possible to combine (add) two trinomials and end up with a binomial answer.


2. Explain why the degree of the term
x +4⁵ is not 5. What is the degree?
3. Can the sum of two polygons in x, both of degree 4, be of degree 3? If so give an example.
4. Choose one or more of the following descriptions for each expressions. (a) polynomial, (b) polynomial written in descending order, (c) not a polynomial.
i) -6w³+ 7w² + 2w -11
ii) x⁵ + x⁹
iii) 4y³ - 3y + 2/y
iv) 3a⁵ -2a³ - 6a^-1 + 15
v) j^-1
vi) k⁶ - k⁴ + 3k - 2

These are very good problems that can teach you a great deal.
What have you done to start these?