Remainder & Factor Theorems 3/30/20 Assignment

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

How do you perform synthetic substitution?

Back

To perform synthetic substitution, write down the coefficients of the polynomial, use the value of x to be substituted, and follow the synthetic division process.

Front

What is synthetic division?

Back

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

Front

If g(x) = 2x^4 + 7x^3 - 6x^2 + 20, what is g(-4)?

Back

g(-4) = -12.

Front

What is the remainder when dividing (3x^3 - 5x^2 - 4x + 1) by (x + 3)?

Back

The remainder is -113.

Front

What does it mean if the remainder is 0 when dividing two polynomials?

Back

If the remainder is 0, it means that the divisor is a factor of the dividend.

Front

How do you determine if (x + 2) is a factor of a polynomial?

Back

Use synthetic division or the Remainder Theorem. If the remainder is 0, then (x + 2) is a factor.

Front

What is the result of synthetic division of x^4 + x^3 - 2x^2 + 3x + 7 by (x + 2)?

Back

The remainder is 1, so (x + 2) is not a factor.

Front

What is the significance of the remainder in polynomial division?

Back

The remainder indicates how much is left over after division and can help determine factors.