Synthetic and Long division

Front

What is synthetic division?

Back

A method for dividing a polynomial by a linear binomial of the form (x - c) using coefficients.

Front

What is long division in polynomials?

Back

A process similar to numerical long division, used to divide polynomials by polynomials.

Front

What is the remainder theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

How do you find the remainder of (4x^3 - 3x^2 - 4x + 2) ÷ (x - 3)?

Back

Evaluate f(3) = 4(3)^3 - 3(3)^2 - 4(3) + 2 = 71.

Front

What is the result of (2x^3 + 7x^2 - 6x - 8) ÷ (x + 4)?

Back

The quotient is 2x^2 - x - 2.

Front

What does it mean to use a zero placeholder in synthetic division?

Back

It means to include a coefficient of 0 for any missing degree terms in the polynomial.

Front

What is the proper way to express the answer of a polynomial division?

Back

The answer should be in the form of a polynomial plus a remainder over the divisor.

Front

What is the significance of the leading coefficient in polynomial division?

Back

It determines the highest degree term in the quotient.

Front

How do you perform synthetic division for (x^4 + 3x^2 - 4x - 2) ÷ (x - 2)?

Back

Use 2 as the divisor and write coefficients: 1, 0, 3, -4, -2.

Front

What is the first step in long division of polynomials?

Back

Divide the leading term of the dividend by the leading term of the divisor.