Factoring Trinomials

Front

What is factoring in algebra?

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 a trinomial?

Back

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

Front

What does GCF stand for, and what does it mean?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers or terms.

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b, then express the trinomial as (x + m)(x + n), where m and n are those two numbers.

Front

What is the difference between a perfect square trinomial and a regular trinomial?

Back

A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, while a regular trinomial does not necessarily have this property.

Front

What is the factored form of a perfect square trinomial?

Back

The factored form of a perfect square trinomial is (a + b)² or (a - b)², where a and b are the terms of the binomial.

Front

How do you factor the expression k² - 2k - 24?

Back

To factor k² - 2k - 24, find two numbers that multiply to -24 and add to -2. The factors are (k + 4)(k - 6).

Front

What is the process to factor the expression 3x² + 5x - 12?

Back

To factor 3x² + 5x - 12, look for two numbers that multiply to (3 * -12) = -36 and add to 5. The factors are (3x - 4)(x + 3).

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 significance of the roots of a polynomial?

Back

The roots of a polynomial are the values of the variable that make the polynomial equal to zero; they are the x-intercepts of the graph of the polynomial.