Factoring a > 1

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What does it mean when a > 1 in factoring?

Back

When a > 1, it indicates that the leading coefficient of a polynomial is greater than one, which affects how the polynomial is factored.

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

How do you factor a quadratic expression when a > 1?

Back

To factor a quadratic expression when a > 1, you can use methods like grouping, the AC method, or trial and error to find two binomials that multiply to the original expression.

Front

What is the AC method in factoring?

Back

The AC method involves multiplying the leading coefficient (a) by the constant term (c) and finding two numbers that multiply to AC and add to b.

Front

What is the first step in factoring a quadratic expression with a > 1?

Back

The first step is to identify the coefficients a, b, and c in the expression ax² + bx + c.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as x + 3 or 2x² - 5.

Front

What is the difference between factoring and expanding?

Back

Factoring is breaking down an expression into its factors, while expanding is multiplying out the factors to get the original expression.

Front

Can you give an example of factoring a quadratic expression with a > 1?

Back

For example, to factor 2x² + 8x + 6, you can factor out a 2 to get 2(x² + 4x + 3), then factor the quadratic to get 2(x + 3)(x + 1).

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient affects the shape of the parabola represented by the quadratic expression and influences the factoring process.