Synthetic Division and the Remainder Theorem Answers
Identify the polynomial divisor, dividend, and quotient represented by the synthetic division. Divisor:
Dividend:
Quotient:
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.
Find the quotient.(2x4 – 3x3 – 6x2 + 11x + 8) ÷ (x – 2)
Select all of the factors of x3 + 5x2 + 2x – 8.
Select all of the roots of x3 + 2x2 – 16x– 32.
The price received for a bicycle is given by the equation b = 100 – 10x2, where x is the number of bicycles produced, in millions.It costs the company $60 to make each bicycle.What is the profit function for the company?
Identify the polynomial divisor, dividend, and quotient represented by the synthetic division. Divisor:
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.
Find the quotient.(2x4 – 3x3 – 6x2 + 11x + 8) ÷ (x – 2)
Select all of the factors of x3 + 5x2 + 2x – 8.
One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. Explain how to find the factors of the polynomial.
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).
Which of the following facts did you include in your explanation? Select all that apply.
Select all of the roots of x3 + 2x2 – 16x– 32.
The price received for a bicycle is given by the equation b = 100 – 10x2, where x is the number of bicycles produced, in millions.It costs the company $60 to make each bicycle.What is the profit function for the company?
A student uses the division shown to divide –3x4 + 15x3 – x + 5 by x – 5, and concludes that x – 5 is not a factor of the polynomial. Describe two errors the student made. Is x – 5 a factor? Explain.
The student made two main errors in the synthetic division setup. First, they used -5 instead of 5 as the value for k (the divisor should be 5 since the factor is x - 5). Second, they did not use a placeholder zero for the missing x^2 term in the polynomial. If the division is performed correctly, the remainder is 0, which means x - 5 is indeed a factor of the polynomial.
Find the quotient.(5x4 – 3x2 + 4) ÷ (x + 1)
Dividend:
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