Select all statements that are true of polynomials:
5a²b-6ab3c + 3a5 is a fifth degree polynomial.
5a²b-6ab3c + 3as has a leading term of 5.
5ab – 6abc + 3acontains three terms.
12x - 10x5 - 7 + 3x4 is equivalent to -10x5 + 3x4 + 12x - 7.
0
12x – 10x5 – 7 + 3x4 has a leading term of -10x5,
12x – 10x5 – 7 + 3x* has a leading coefficient of 12.

True statements are highlighted.

Step-by-step explanation:

⇒ 5a²b - 6ab³c + 3a^5 is a fifth degree polynomial. - It is true.  

Degree of first term is 2 + 1 = 3

Degree of second term is 1 + 3 + 1 = 5

Degree of third term is 5. This is the highest degree and so it is a fifth degree polynomial.

⇒ 5a²b - 6ab³c + 3a^5 has a leading term of 5. - it is false.

Leading term is the term with the highest degree, here it is not 5.

⇒ 5ab - 6abc + 3a contains three terms. - it is true.

Here, there are 3 terms in the polynomial - 5ab, 6abc, 3a

⇒ 12x - 10x^5 - 7 + 3x^4 is equivalent to -10x^5 + 3x^4 + 12x - 7 - it is true.

Rearranging the terms does not change the polynomial.

⇒ 12x - 10x^5 - 7 + 3x^4 has a leading term of -10x^5. - it is true.

Here, the term with the highest degree of x is -10x^5

⇒ 12x - 10x^5 - 7 + 3x^4 has a leading coefficient of 12. - it is false.

Here, the leading term is -10x^5, so leading coefficient is 10.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}