The Binomial Theorem

Question 1

Dividend:

Revolt · Accepted Answer

2x3 + 11x2 + 18x + 9

Question 2

Quotient:

Revolt · Accepted Answer

2x2 + 5x + 3

Question 3

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

Revolt · Accepted Answer

x + 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

Since -3 is a root, x + 3 is a factor. Use synthetic division with -3 and the coefficients 2, 9, 7, and -6. The quotient is 2x^2 + 3x - 2, with remainder 0. Factoring the quotient gives (x + 2)(2x - 1), so the factors of the polynomial are (x + 3)(x + 2)(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.

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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