Dividing Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean for (x - a) to be a factor of a polynomial?

Back

If (x - a) is a factor of a polynomial, then substituting x = a into the polynomial results in a value of zero.

Front

How do you determine if (x - 3) is a factor of 3x^3 + 10x^2 - x - 12?

Back

Substitute x = 3 into the polynomial. If the result is 0, then (x - 3) is a factor.

Front

What is synthetic division?

Back

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

Front

What is the quotient when dividing (21x^2 - 52x + 32) by (7x - 8)?

Back

The quotient is 3x - 4.

Front

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

Back

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

Front

What is the first step in synthetic division?

Back

The first step is to write the coefficients of the polynomial in descending order of degree.

Front

How many zeros are needed in synthetic division for x^6 + 4x^3 + 2?

Back

You need 4 zeros when setting up the top row of synthetic division.

Front

What is the remainder theorem?

Back

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

Front

What is the relationship between factors and roots of a polynomial?

Back

If (x - a) is a factor of a polynomial, then a is a root of the polynomial.