Factoring Trinomials

Front

What is factoring in mathematics?

Back

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

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

To factor completely means to break down an expression into its simplest factors, where no further factoring is possible.

Front

What is the first step in factoring a trinomial?

Back

The first step is to look for a common factor in all the terms of the trinomial.

Front

How do you identify a common factor?

Back

A common factor is a number or variable that divides all terms of the expression without leaving a remainder.

Front

What is the difference of squares?

Back

The difference of squares is a special case of factoring, represented as a² - b² = (a - b)(a + b).

Front

What is the formula for factoring a perfect square trinomial?

Back

The formula is a² ± 2ab + b² = (a ± b)².

Front

How do you factor the expression 3n² - 15n + 18?

Back

First, factor out the common factor 3, then factor the trinomial to get 3(n - 3)(n - 2).

Front

What is the factored form of m² - 81?

Back

The factored form is (m - 9)(m + 9), which is a difference of squares.

Front

What is the factored form of 5v² - 30v + 40?

Back

The factored form is 5(v - 4)(v - 2).