Question

Choose the words or phrases that best complete the sentences. A fifth degree polynomial (must, could) have 5 linear factors. The factors (must, could but don't have to) be distinct.

Answer 1

'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'.

Answer 2

First of all, a fifth degree polynomial means that the term with the highest degree is five.
so,

A fifth degree polynomial could have 5 linear factors. The factors could but don't have to be distinct.