Polynomial Division

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial of the same or lower degree, resulting in a quotient and a remainder.

Front

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

Back

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

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division used when dividing by a linear factor of the form (x - c).

Front

What number is used in the left-hand box for synthetic division when dividing by (x - 2)?

Back

The number used is 2.

Front

What is the quotient when dividing x^3 - 3x^2 - 10x + 24 by (x + 3)?

Back

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

Front

How do you determine if a number k is a zero of a polynomial function f(x)?

Back

A number k is a zero of f(x) if f(k) = 0.

Front

What is the result of dividing -2x^2 + 4x + 48 by (x + 4)?

Back

The result is -2x + 12.

Front

What is the remainder theorem in polynomial division?

Back

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

Front

What is the significance of the degree of a polynomial in division?

Back

The degree of a polynomial determines the highest power of the variable in the polynomial, which affects the division process and the resulting quotient.

Front

What is the relationship between zeros of a polynomial and its factors?

Back

If k is a zero of a polynomial f(x), then (x - k) is a factor of f(x).