12/09 (LSAE 12/05)

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What is the difference between a prime number and a composite number?

Back

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A composite number is a natural number greater than 1 that has more than two positive divisors.

Front

Factor the expression: 3x² - 75

Back

3(x + 5)(x - 5)

Front

Factor the expression: 4x² - 9

Back

(2x - 3)(2x + 3)

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

Factor completely: 3n² - 15n + 18

Back

3(n - 3)(n - 2)

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

Factor the expression: 3v² - 4v - 7

Back

(3v - 7)(v + 1)

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are no real roots.