I thank you for helping me Question 1 5 points What is the m

I thank you for helping me.

Question 1 (5 points)

What is the middle term in the expansion of (x - 4)⁴?

Question 2 (5 points)

Simplify. (4x + 3)(x² - 2x + 8)

Question 3 (5 points)

Divide (27x⁴ - 12x³ + 3x²) by (3x²).

Question 4 (5 points)

How many zeros may we expect of the polynomial P(x) = 3x⁴ - x² + 5?

Question 5 (5 points)

Divide the following polynomials: (6x⁵ + 4x⁴ – x³ + 4x² - 5) ÷ (2x² + 1)

Question 6 (5 points)

Solve. x⁴ + 3x³ - 6x² + 17x – 15 = 0

Question 7 (5 points)

Find the remainder when 2x³ - 3x + 1 is divided by x + 3.

Question 8 (5 points)

Find roots of the polynomial P(x) = x³ + 4x² - 4x - 16

Question 9 (5 points)

List all the possible rational roots for the polynomial P(x) = 2x³ + x² - 5x + 6.

Question 10 (5 points)

Which of the following combinations is NOT a combination of possible positive, negative and imaginary roots for the polynomial function P(x) = 4x⁴ - 3x² + x + 1

2 pos. & 2 Imaginary

2 neg. & 2 imaginary

2 pos. & 2 neg.

1 pos., 1 neg. & 2 imaginary

Question 11 (5 points)

Divide the following polynomials: (5x³ + 2x² - 4x + 7) ÷ (x - 2)

a)

b)

c)

d)

Question 12 (5 points)

Which of the following polynomials has zeros of -4, -1/2, 2/3?

Question 12 options:

a)

P(x) = 6x³ + 31x² + 30x + 8

b)

P(x) = 6x³ + 23x² - 6x - 8

c)

P(x) = 6x³ - 31x² + 30x - 8

d)

P(x) = 6x³ + 23x + 30x + 8

Question 13 (5 points)

How many terms are in the expansion of (2x - 5y)⁵?

Question 14 (5 points)

Find the zeros of the polynomial P(x) = x⁴ - x³ - 15x² + 9x + 54.

Question 14 options:

a)

x = 3, ±2

b)

x = -3, ±2

c)

x = -2, ±3

d)

x = 2, ±3

Question 15 (5 points)

Which of the following binomials is a factor of x⁴ - 5x³ - 10x² + 20x + 24?

Question 15 options:

a)

x + 2

b)

x - 3

c)

both a and b

d)

neither a nor b

Question 16 (5 points)

Simplify. (5x³ - 2x + 4) – (3x² - x + 9)

Question 17 (5 points)

Solve.   x³ - 2x² + x – 2 = 0

Question 18 (5 points)

Which of the following operations are closed under polynomials?

Question 18 options:

a)

subtraction and division

b)

addition, subtraction and division

c)

addition, subtraction and multiplication

d)

multiplication and division

Question 19 (10 points)

Mary’s Algebra II assignment contains the following question: Expand (2x - 3)³.

After considering the question, Mary remembers that she needs to use Pascal’s triangle to help her expand the binomial. She looks at the third row and finds the numbers 1, 2 and 1 which she knows are the coefficients of the expansion.

Next, she remembers that the first term begins with the zero power and counts up and the second term begins with the binomial’s exponent, in this case 3, and counts down.  

Her answer, then, is as follows:

(2x - 3)³ = 1(2x)⁰(-3)³ + 2(2x)¹(-3)² + 1(2x)²(-3)¹ = -27 + 36x - 12x²

Mary asks you to check her work. Write a paragraph to Mary explaining her mistakes and giving the correct solution.

Once again, thank you!

	a)
	b)
	c)
	d)

Solution

Dear Student

Thank you for using chegg !!

General formula for binomial expansion is given by

(X + a ) ^n = nC0 x^n a^ 0 + nC1x^(n-1)a^1 +.........nCn x^0a^n

For given expression (1-x)^4 middle term will be 4/2 = 2

Therefore term is

4C2 1^2 (-x)^2

=6x^2