Synthetic Division and Polynomial Coefficients

What is the primary purpose of synthetic division?

• To multiply polynomials quickly.

• To find the roots of any polynomial.

• To divide a polynomial by a linear polynomial.

• To factorize quadratic equations.

What is the coefficient form of the polynomial x^4 + 2x^3 + 3x^2 + 4x + 5?

• (4, 3, 2, 1, 0)

• (1, 2, 3, 4, 5)

• (x, 2x, 3x, 4x, 5)

• (1, 2, 3, 4, 5, 0)

When dividing a polynomial by (x + 2) using synthetic division, what value should be used as the divisor in the synthetic division setup?

• +2

• -2

• x

• 1

What is the first step in performing synthetic division after setting up the coefficients and the divisor?

• Multiply the first coefficient by the divisor.

• Add the first two coefficients.

• Bring down the first coefficient.

• Divide the first coefficient by the divisor.

What is the remainder when (x^4 + 2x^3 + 3x^2 + 4x + 5) is divided by (x + 2) using synthetic division?

• 0

• -2

• 4

• 9