Question

consider:
$q(x) = 5x^3 - 4x + 12 - x^2$

1. rewrite $q(x)$ in standard form (descending powers of $x$).
2. after rewriting, identify the leading term and leading coefficient.
3. what is the degree of $q(x)$?
4. how many terms does $q(x)$ have? classify it: monomial, binomial, trinomial, or polynomial (4+ terms).

Explanation:

Step1: Rearrange terms by degree

$Q(x) = 5x^3 - x^2 - 4x + 12$

Step2: Identify leading term/coefficient

Leading term: $5x^3$, Leading coefficient: $5$

Step3: Find highest exponent (degree)

Highest power of $x$ is $3$

Step4: Count terms and classify

Count terms: $5x^3, -x^2, -4x, 12$ (4 terms)

Answer:

1. $Q(x) = 5x^3 - x^2 - 4x + 12$
2. Leading term: $5x^3$; Leading coefficient: $5$
3. $3$
4. 4 terms; polynomial (4+ terms)