Answer:
[1]
Given: ![(5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)](https://tex.z-dn.net/?f=%285x%5E3%20%2B%203x%5E2%20-%207x%20%2B%2010%29%20-%20%283x%5E3%20-%20x%5E2%20%2B%204x%20-%201%29)
Remove the parenthesis, we get;
![(5x^3 + 3x^2 - 7x + 10) - (3x^3-x^2+ 4x -1)](https://tex.z-dn.net/?f=%285x%5E3%20%2B%203x%5E2%20-%207x%20%2B%2010%29%20-%20%283x%5E3-x%5E2%2B%204x%20-1%29)
![5x^3 + 3x^2 - 7x + 10- 3x^3 + x^2- 4x + 1](https://tex.z-dn.net/?f=5x%5E3%20%2B%203x%5E2%20-%207x%20%2B%2010-%203x%5E3%20%2B%20x%5E2-%204x%20%2B%201)
Like terms are the those terms with same variable and powers.
Combine like terms;
![2x^3 + 4x^2 - 11x + 11](https://tex.z-dn.net/?f=2x%5E3%20%2B%204x%5E2%20-%2011x%20%2B%2011)
To write this polynomial in standard form, you write starting with the term with the highest degree, or exponent(i.e
), and then in decreasing order .
Standard form: ![2x^3 + 4x^2 - 11x + 11](https://tex.z-dn.net/?f=2x%5E3%20%2B%204x%5E2%20-%2011x%20%2B%2011)
To, classify a polynomial by degree, you just look at the highest exponent, or degree.
Since, 3 is the highest degree (
), it is a cubic.
Now, classify a polynomial by the number of terms, count how many terms are in the polynomial(
)
Number of terms: 4 (so this is polynomial)
[2]
Similarly,
for ![(9w - 4w^2 + 10) + (8w^2 + 7 + 5w)](https://tex.z-dn.net/?f=%289w%20-%204w%5E2%20%2B%2010%29%20%2B%20%288w%5E2%20%2B%207%20%2B%205w%29)
Remove the parenthesis, we get;
![9w - 4w^2 + 10+ 8w^2 + 7 + 5w](https://tex.z-dn.net/?f=9w%20-%204w%5E2%20%2B%2010%2B%208w%5E2%20%2B%207%20%2B%205w)
Combine like terms; we have
![14w + 4w^2 + 17](https://tex.z-dn.net/?f=14w%20%2B%204w%5E2%20%2B%2017)
Standard form: ![4w^2 + 14w + 17](https://tex.z-dn.net/?f=%204w%5E2%20%2B%2014w%20%2B%2017)
Degree of the polynomial is, 2
Number of terms: 3 ( so, this is trinomial)