Answer:
'A fifth degree polynomial could have 5 linear factors'.
'The factors could but don't have to be distinct'.
Step-by-step explanation:
Given : Statements
'A fifth degree polynomial (must, could) have 5 linear factors'.
'The factors (must, could but don't have to) be distinct'.
To find : Choose the words or phrases that best complete the sentences.
Solution :
According to fundamental theorem of polynomial states that every polynomial of m>0 degree has exactly m zeroes.
So, 5 degree polynomial has exactly 5 zeros.
i.e. 'A fifth degree polynomial could have 5 linear factors'.
But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.
So, the factors could be distinct or similar.
i.e. 'The factors could but don't have to be distinct'.
