Remainder and Factor Theorem

Front

What is the Remainder Theorem?

Back

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

Front

What is the Factor Theorem?

Back

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

Front

How do you find the value of k so that a linear expression is a factor of a polynomial?

Back

To find k, substitute the value of x from the linear expression into the polynomial and set the equation equal to zero, then solve for k.

Front

What is the relationship between factors and remainders in polynomial division?

Back

If a polynomial is divided by a factor, the remainder will be zero.

Front

What does it mean if (x - 3) is not a factor of a polynomial?

Back

It means that when the polynomial is evaluated at x = 3, the result is not zero.

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

Back

Evaluate the polynomial at the value corresponding to the factor; if the result is zero, then it is a factor.

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What is the process to find the remainder when dividing a polynomial by a linear divisor?

Back

Use the Remainder Theorem: evaluate the polynomial at the value that makes the divisor zero.

Front

What is the significance of the value of P(a) in polynomial division?

Back

P(a) gives the remainder when P(x) is divided by (x - a).

Front

How can you verify if a polynomial is divisible by a certain factor?

Back

Perform polynomial long division or synthetic division and check if the remainder is zero.

Front

What is synthetic division and when is it used?

Back

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