Short Factoring Flashcard

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 does it mean for a polynomial to be prime?

Back

A polynomial is considered prime if it cannot be factored into the product of two non-constant polynomials.

Front

How do you factor a quadratic expression of the form ax^2 + bx + c?

Back

To factor a quadratic expression, look for two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the expression using these numbers and factor by grouping.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a - b)(a + b).

Front

How do you factor the expression 5x^2 - 12x + 7?

Back

To factor 5x^2 - 12x + 7, find two numbers that multiply to (5*7) = 35 and add to -12. The factors are -5 and -7, so it can be factored as (5x - 7)(x - 1).

Front

What is the factored form of 9x^2 - 1?

Back

The expression 9x^2 - 1 can be factored using the difference of squares formula: 9x^2 - 1 = (3x - 1)(3x + 1).

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for a greatest common factor (GCF) among the terms.

Front

What is the significance of the leading coefficient in a quadratic expression?

Back

The leading coefficient (the coefficient of the highest degree term) affects the direction of the parabola and the nature of the roots of the quadratic equation.

Front

What are the possible methods for factoring polynomials?

Back

Common methods for factoring polynomials include factoring by grouping, using the quadratic formula, and applying special product formulas (like difference of squares and perfect square trinomials).

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, such as a^2 + 2ab + b^2 = (a + b)^2.