Factor Theorem

Front

What is the Factor Theorem?

Back

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

Front

How do you determine if (x - 1) is a factor of f(x) = x^3 + 4x^2 + x - 6?

Back

Evaluate f(1). If f(1) = 0, then (x - 1) is a factor.

Front

What does it mean if f(c) = 0 for a polynomial f(x)?

Back

It means that (x - c) is a factor of the polynomial.

Front

If f(x) = x^3 + 4x^2 + x - 6, what is f(1)?

Back

f(1) = 1^3 + 4(1^2) + 1 - 6 = 0, so (x - 1) is a factor.

Front

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

Back

f(2) = 2^3 + 4(2^2) + 2 - 6 = 20, so (x - 2) is not a factor.

Front

What is the result of evaluating f(x) = 4x^3 + 21x^2 + 5x + 10 at x = -5?

Back

f(-5) = 10.

Front

Which binomial is a factor of f(x) = x^3 + x^2 - 24x + 36?

Back

x + 6 is a factor.

Front

Which binomial is a factor of f(x) = x^3 - 6x^2 + 3x + 10?

Back

x + 1 is a factor.

Front

What is the significance of finding a factor of a polynomial?

Back

Finding a factor helps in simplifying the polynomial and solving equations.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.