The Binomial Theorem

Question 1

Identify the polynomial divisor, dividend, and quotient represented by the synthetic division. Divisor:

Revolt · Accepted Answer

x + 3

Question 2

Dividend:

Revolt · Accepted Answer

2x3 + 11x2 + 18x + 9

Question 3

Quotient:

Revolt · Accepted Answer

2x2 + 5x + 3

Question 4

Use synthetic division to find the expression for the area of the base of a rectangular prism with height x + 4 and volume x3 + 2x2 – 17x – 36.

Revolt · Accepted Answer

x2 – 2x – 9

Question 5

Find the quotient.(2x4 – 3x3 – 6x2 + 11x + 8) ÷ (x – 2)

Revolt · Accepted Answer

mc001-2.jpg

Question 6

Find the quotient.(5x4 – 3x2 + 4) ÷ (x + 1)

Revolt · Accepted Answer

mc002-1.jpg

Question 7

Select all of the factors of x3 + 5x2 + 2x – 8.

Revolt · Accepted Answer

x + 4; x – 1; x + 2

Question 8

One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. Explain how to find the factors of the polynomial.

Revolt · Accepted Answer

Identify the factor x + 3 from the given root –3. Use synthetic division to divide the polynomial by x + 3. Use the bottom row of the synthetic division as coefficients in the quadratic 2x2 + 3x – 2. Factor the quotient to find the two other factors: x + 2 and 2x – 1.

Question 9

Which of the following facts did you include in your explanation? Select all that apply.

Revolt · Accepted Answer

Identify the factor x + 3 from the given root –3.; Use synthetic division to divide the polynomial by x + 3.; Use the bottom row of the synthetic division as coefficients in the quadratic 2x2 + 3x – 2.; Factor the quotient to find the two other factors: x + 2 and 2x – 1.

Question 10

Select all of the roots of x3 + 2x2 – 16x– 32.

Revolt · Accepted Answer

–2; –4; 4

The Binomial Theorem Answers

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