Question

the _______________ term of a polynomial is the term with the highest degree of the variable.
multiplying ( x ) by ( x^2 + 4 ) and then adding ( 3x ) times ( x^2 + 4 ) demonstrates the use of the _______________ property.
to simplify the expression ( left( \frac{1}{2}x
ight)(2x^2 - 3x + 4) ) after applying the distributive property, one must _______________ the resulting terms.

Explanation:

1. In polynomials, the term with the highest variable degree is defined as the leading term.
2. The described operation follows the distributive property, which states $a(b+c)=ab+ac$ (here applied to factor out $x^2+4$ from $x(x^2+4)+3x(x^2+4)$).
3. After applying the distributive property to expand the expression, the next step to simplify is combining like terms (terms with the same variable raised to the same power).

Answer:

1. Leading
2. Distributive
3. Combine like