Polynomial Division

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial, similar to long division with numbers.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c).

Front

In synthetic division, what does the left-hand box represent?

Back

The left-hand box in synthetic division represents the value of 'c' from the divisor (x - c).

Front

How do you set up synthetic division for x^6 + 4x^3 + 2?

Back

You need to include 4 zeros in the top row to account for the missing degrees of x.

Front

What is the result of (2x^3 - 5x - 7) ÷ (x - 2)?

Back

The result is (2x^2 + 4x + 3) - 1/(x-2).

Front

What is the order of polynomial coefficients in (3x - 4x^3 + 6x^4 + 1) / (x + 3)?

Back

The order of coefficients is 6, -4, 0, 3, 1.

Front

What is the quotient of (x^3 - 3x^2 - 10x + 24) ÷ (x + 3)?

Back

The quotient is x^2 - 6x + 8.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is a linear divisor in polynomial division?

Back

A linear divisor is a polynomial of degree one, typically in the form (x - c).

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).