Question

a mathematical expression consisting of variables, exponents, and coefficients, which includes terms that are summed or subtracted, is called a ___________. in polynomial multiplication, terms that share the same variables raised to the same power are referred to as _________ terms. the result of multiplying the monomial ( 3x ) by the polynomial ( (x^2 - x + 2) ) should be simplified by combining ___________.

Explanation:

1. A polynomial is defined as a mathematical expression made up of variables, coefficients, and exponents, with terms combined via addition or subtraction.
2. In polynomial operations, "like terms" are terms that have identical variables raised to the exact same powers, which can be combined.
3. When multiplying \(3x\) by \((x^2 - x + 2)\), we first distribute to get \(3x^3 - 3x^2 + 6x\); since there are no like terms here, the general step for such multiplications is combining like terms to simplify the result.

Answer:

1. polynomial
2. like
3. like terms