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?
Which of the following facts did you include in your explanation? Select all that apply.
Which of the following facts did you include in your response? Select all that apply.
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.
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).
Find the quotient.(5x4 – 3x2 + 4) ÷ (x + 1)
Did you find these answers helpful?
TRY EDGENUITY HACKS
- Auto Complete Exams
- Auto Complete Assignments
- Skip Videos Instantly