Question

Select all statements that are true of polynomials:

5a²b – 6ab3c + 3a5 is a fifth degree polynomial.

2b-6ab3c + 3a5 has a leading term of 5.

5a²b – 6ab3c + 3a5 contains three terms.

12x – 10x5 – 7 + 3x4 is equivalent to -10x5 + 3x4 + 12x -

12x - 10x5 – 7 + 3x4 has a leading term of -10x5.

12

105 72.4

Answer 1

The Statements have been categorized and explanation given.

Explanation:

The following statements are true

`5a\²b - 6ab^3c + 3a^5` is a fifth degree polynomial.

• The degree of a polynomial is the highest power in the polynomial, therefore,
  `5a\²b - 6ab^3c + 3a^5` is a fifth degree polynomial.

`5a\²b - 6ab^3c + 3a^5` contains three terms.

• This is true. The terms are:
  `5a\²b, - 6ab^3c, 3a^5`

`12x -10x^5 - 7 + 3x^4` is equivalent to
`-10x^5 + 3x^4 + 12x -7`

• The second polynomial is a basic rearrangement of the first polynomial, therefore the statement is true.

`12x - 10x^5 - 7 + 3x^4` has a leading term of
`-10x^5.`

• The leading term is the term containing the highest power. The highest power is 5 and the term containing it is
  `-10x^5.`

FALSE

`2b-6ab^3c + 3a^5` has a leading term of 5.

The leading term of this polynomial is
`3a^5`