Six statements about polynomials are given. Select all the statements that are true.(4 points)

Question

Responses

5a^2b−6ab^3c+3a^5
is a fifth degree polynomial.
5 A squared b minus 6 A b cubed c plus 3 A to the 5th power is a fifth degree polynomial.

5a2b−6ab3c+3a5
has a leading coefficient of 5.
5 A squared b minus 6 A b cubed c plus 3 A to the 5th power has a leading coefficient of 5.

5a2b−6ab3c+3a5
contains three terms.
5 A squared b minus 6 A b cubed c plus 3 A to the 5th power contains three terms.

12x−10x5−7+3x4
has a leading coefficient of 12.
12 x minus 10 x to the 5th power minus 7 plus 3 x to the 4th power has a leading coefficient of 12.

12x−10x5−7+3x4
is equivalent to −10x5+3x4+12x−7
12 x minus 10 x to the 5th power minus 7 plus 3 x to the 4th power is equivalent to negative 10 x to the 5th power plus 3 x to the 4th power plus 12 x minus 7

12x−10x5−7+3x4
has a leading term of −10x5

Answer 1

Let's evaluate each statement one by one:

1. 5a²b - 6ab³c + 3a⁵ is a fifth degree polynomial.

   • True. The highest degree of the terms is 5 from the term 3a⁵.

2. 5a²b - 6ab³c + 3a⁵ has a leading coefficient of 5.

   • False. The leading term (the term with the highest degree) is 3a⁵, which has a leading coefficient of 3, not 5.

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

   • True. This polynomial contains three distinct terms: 5a²b, -6ab³c, and 3a⁵.

4. 12x - 10x⁵ - 7 + 3x⁴ has a leading coefficient of 12.

   • False. The leading term is -10x⁵, which has a leading coefficient of -10.

5. 12x - 10x⁵ - 7 + 3x⁴ is equivalent to -10x⁵ + 3x⁴ + 12x - 7.

   • True. This statement correctly represents the same polynomial rearranged.

6. 12x - 10x⁵ - 7 + 3x⁴ has a leading term of -10x⁵.

   • True. The leading term of this polynomial is indeed -10x⁵.

Summary:

The true statements are:

• 5a²b - 6ab³c + 3a⁵ is a fifth degree polynomial.
• 5a²b - 6ab³c + 3a⁵ contains three terms.
• 12x - 10x⁵ - 7 + 3x⁴ is equivalent to -10x⁵ + 3x⁴ + 12x - 7.
• 12x - 10x⁵ - 7 + 3x⁴ has a leading term of -10x⁵.