Question

Given the vocabulary terms and their definitions, match the correct terms to their corresponding definitions:

a. factor theorem
b. multiplicity
c. polynomial long division
d. remainder theorem
e. standard form of a polynomial
f. synthetic division

Definitions:
___16. A polynomial that has terms written in descending order by a linear binomial.
___17. The simplified form of division of a polynomial by a linear binomial.
___18. When the same solution occurs more than once.
___19. Dividing polynomial P(x) by (x-a) yields a remainder whose value is the same as P(a).

Answer 1

The correct matches for the definitions provided are: e. standard form of a polynomial, f. synthetic division, b. multiplicity, and d. remainder theorem.

Step-by-step explanation:

Given the definitions, the correct terms can be matched as follows:

• e. standard form of a polynomial: A polynomial that has terms written in descending order by degree. (16)
• f. synthetic division: The simplified form of division of a polynomial by a linear binomial. (17)
• b. multiplicity: When the same solution occurs more than once. (18)
• d. remainder theorem: Dividing polynomial P(x) by (x-a) yields a remainder whose value is the same as P(a). (19)

Note: The factor theorem (a) and polynomial long division (c) definitions are not provided, hence they are not matched here.