College Algebra Review

Front

What is the property of logarithms that allows you to condense a sum of logs into a single log?

Back

The property is called the Product Rule: log_b(M) + log_b(N) = log_b(M*N).

Front

What does it mean to factor a polynomial completely?

Back

Factoring completely means expressing the polynomial as a product of its irreducible factors, which cannot be factored further over the given number system.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap the x and y in the equation and solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What is the property of logarithms that allows you to expand a log?

Back

The property is called the Power Rule: log_b(M^p) = p * log_b(M).

Front

What are the roots of a polynomial?

Back

The roots are the values of x for which the polynomial equals zero.

Front

What is the Quadratic Formula used for?

Back

The Quadratic Formula is used to find the roots of a quadratic equation in the form ax^2 + bx + c = 0: x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.8.NS.A.1

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number: log_b(a) = c means b^c = a.

Tags

CCSS.HSF.BF.B.5

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions are the inverse of logarithmic functions. If y = b^x, then x = log_b(y).

Tags

CCSS.HSF.BF.B.5

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B