1st Semester Review (Part 1) - Algebra 2

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or root) of a polynomial equation, in the form of p/q, is such that p is a factor of the constant term and q is a factor of the leading coefficient.

Front

How do you factor a difference of squares?

Back

A difference of squares can be factored using the formula a² - b² = (a + b)(a - b). For example, q² - 121 can be factored as (q + 11)(q - 11).

Front

What does it mean for (x - 2) to be a factor of a polynomial?

Back

If (x - 2) is a factor of a polynomial f(x), then f(2) = 0, meaning that substituting x = 2 into the polynomial results in zero.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

What are complex numbers?

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit (i² = -1).

Front

How do you simplify the expression (x² - 4)/(x + 2)?

Back

You can simplify (x² - 4) as (x + 2)(x - 2), so (x² - 4)/(x + 2) simplifies to x - 2, provided x ≠ -2.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

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 of the form (x - c).

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).