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