Factoring

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 the factored form of a quadratic equation?

Back

The factored form of a quadratic equation ax^2 + bx + c is (px + q)(rx + s), where p, q, r, and s are constants.

Front

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

Back

To factor a quadratic expression of the form x^2 + bx + c, find two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n), where m and n are the two numbers.

Front

What is the difference between factoring by grouping and other factoring methods?

Back

Factoring by grouping involves rearranging terms in a polynomial to create groups that can be factored separately, while other methods may involve direct application of formulas or patterns.

Front

What is the first step in factoring by grouping?

Back

The first step in factoring by grouping is to group the terms of the polynomial into pairs or sets that can be factored individually.

Front

What is a common factor in factoring?

Back

A common factor is a number or variable that divides each term of a polynomial, which can be factored out to simplify the expression.

Front

How do you factor a polynomial with a common factor?

Back

To factor a polynomial with a common factor, identify the greatest common factor (GCF) of all terms, then divide each term by the GCF and express the polynomial as GCF multiplied by the resulting polynomial.

Front

What is the significance of the zero product property in factoring?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero, which is used to solve equations after factoring.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

The factored form of the expression x^2 - 9 is (x - 3)(x + 3), which is an example of the difference of squares.

Tags

CCSS.HSA.APR.C.4

Front

What is the process for factoring a cubic polynomial?

Back

To factor a cubic polynomial, look for a common factor, use synthetic division or long division to factor out a linear term, and then factor the resulting quadratic expression.