Factoring (when a>1)

Front

What is factoring in algebra?

Back

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

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, such that no further factoring is possible.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you identify the coefficients in a quadratic expression?

Back

In the expression ax² + bx + c, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the first step in factoring a trinomial?

Back

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

Front

What is the purpose of finding two numbers that multiply to ac and add to b in factoring?

Back

These two numbers help in splitting the middle term to facilitate factoring by grouping.

Front

What is the difference between factoring by grouping and using the quadratic formula?

Back

Factoring by grouping involves rearranging and grouping terms to find factors, while the quadratic formula provides a direct solution for finding roots.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (a) affects the shape of the parabola and influences the factoring process, especially when a > 1.

Front

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

Back

You can use the method of splitting the middle term or apply the quadratic formula to find the roots and then express the quadratic as a product of its factors.