Factoring Intro - X Game

Front

What is factoring in mathematics?

Back

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

Front

What is a factor?

Back

A factor is a number or algebraic expression that divides another number or expression evenly, without leaving a remainder.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it in the form (x - p)(x - q), where p and q are the roots of the equation.

Front

What is the relationship between the roots and factors of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a factor of the polynomial.

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots of a quadratic equation using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients of the equation.

Front

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

Back

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

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for a common factor among all the terms.

Front

What is the difference between prime and composite numbers?

Back

A prime number has exactly two distinct positive divisors: 1 and itself, while a composite number has more than two positive divisors.

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

How can you check if your factoring is correct?

Back

You can check your factoring by multiplying the factors back together to see if you obtain the original expression.