Remainder and Factor theorem

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial p(x) by (x - c) is equal to p(c).

Front

What is the Factor Theorem?

Back

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

Front

How do you find the remainder when dividing a polynomial by a linear factor?

Back

To find the remainder when dividing p(x) by (x - c), evaluate p(c).

Front

What is the remainder when a^3 - 4 is divided by a + 2?

Back

-12

Front

What is the remainder when p(x) = x^3 - 5x^2 + 2x - 10 is divided by (x - 5)?

Back

0

Front

Find the value of k when x^3 - 2kx^2 + 3x - 1 is divided by x - 1 and the remainder is -3.

Back

k = 3

Front

Divide (n² + 10n + 18) by (n + 5). What is the result?

Back

n + 5 with a remainder of -7.

Front

Is (x + 2) a factor of the polynomial x^4 + x^3 - 2x^2 + 3x + 7?

Back

No, the remainder is 1.

Front

What is the significance of a remainder of 0 in polynomial division?

Back

A remainder of 0 indicates that the divisor is a factor of the polynomial.

Front

How can you determine if a polynomial has a specific factor?

Back

Evaluate the polynomial at the root of the factor; if the result is 0, it is a factor.