Answer:
[1]
Given: [tex](5x^3 + 3x^2 - 7x + 10) - (3x^3 - x^2 + 4x - 1)[/tex]
Remove the parenthesis, we get;
[tex](5x^3 + 3x^2 - 7x + 10) - (3x^3-x^2+ 4x -1)[/tex]
[tex]5x^3 + 3x^2 - 7x + 10- 3x^3 + x^2- 4x + 1[/tex]
Like terms are the those terms with same variable and powers.
Combine like terms;
[tex]2x^3 + 4x^2 - 11x + 11[/tex]
To write this polynomial in standard form, you write starting with the term with the highest degree, or exponent(i.e [tex]x^3[/tex]), and then in decreasing order .
Standard form: [tex]2x^3 + 4x^2 - 11x + 11[/tex]
To, classify a polynomial by degree, you just look at the highest exponent, or degree.
Since, 3 is the highest degree ([tex]x^3[/tex]), it is a cubic.
Now, classify a polynomial by the number of terms, count how many terms are in the polynomial( [tex]2x^3 + 4x^2 - 11x + 11[/tex])
Number of terms: 4 (so this is polynomial)
[2]
Similarly,
for [tex](9w - 4w^2 + 10) + (8w^2 + 7 + 5w)[/tex]
Remove the parenthesis, we get;
[tex]9w - 4w^2 + 10+ 8w^2 + 7 + 5w[/tex]
Combine like terms; we have
[tex]14w + 4w^2 + 17[/tex]
Standard form: [tex] 4w^2 + 14w + 17[/tex]
Degree of the polynomial is, 2
Number of terms: 3 ( so, this is trinomial)
