Dividing polynomials

Front

What is synthetic division?

Back

A method used to divide a polynomial by a linear divisor of the form (x - c) using coefficients.

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial in descending order.

Front

How do you determine the number to place in the left-hand box during synthetic division?

Back

The number is the root of the divisor (x - c), which is c.

Front

Divide: (x^3 + 3x^2 - 4x - 12) by (x^2 + x - 6)

Back

x + 2

Front

What is the result of dividing (4x^2 - 24x + 35) by (2x - 5)?

Back

2x - 7

Front

What is the remainder when dividing (6b^2 - 5b - 52) by (3b - 10)?

Back

The remainder is 2.

Front

What is the quotient of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

x^2 + 2x - 6 with a remainder of 27.

Front

What does it mean if a polynomial is divisible by another polynomial?

Back

It means that the division results in a polynomial with no remainder.

Front

What is the degree of a polynomial?

Back

The highest power of the variable in the polynomial.

Front

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

Back

It affects the end behavior of the polynomial graph.