PreCalculus Sem 1 Review

Front

What are the zeros of the polynomial function x^3 - x^2 - 10x - 8?

Back

The zeros are -1, -2, and 4.

Front

What is the radius of the circle given by the equation x² + y² - 10x + 8y - 23 = 0?

Back

The radius is 8.

Front

Completely factor the expression x^3 + 64.

Back

The factored form is (x + 4)(x^2 - 4x + 16).

Front

Using the Rational Zero Theorem, solve the equation 2x^3 - 11x^2 + 12x + 9 = 0.

Back

The solutions are -1/2, 3, and 3.

Front

Using the Rational Zero Theorem, solve the equation x^3 + 3x^2 - 6x - 8 = 0.

Back

The solutions are -4, -1, and 2.

Front

What is the Rational Zero Theorem?

Back

The Rational Zero Theorem states that any rational solution of a polynomial equation can be expressed as p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x using factoring, synthetic division, or the quadratic formula.

Front

What is the standard form of a circle's equation?

Back

The standard form is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

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.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction.