Factoring by Grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors and then factoring out the common binomial.

Front

What is the first step in factoring by grouping?

Back

The first step is to rearrange the polynomial into two groups that can be factored separately.

Front

How do you determine if a polynomial can be factored by grouping?

Back

A polynomial can be factored by grouping if it can be rearranged into two or more groups that share a common factor.

Front

What is a common factor in the context of polynomials?

Back

A common factor is a number or variable that divides each term of the polynomial without leaving a remainder.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial is an expression that is written as a product of its factors.

Front

How do you check if a factor is correct?

Back

To check if a factor is correct, multiply the factors back together to see if you obtain the original polynomial.

Front

What is the significance of the distributive property in factoring?

Back

The distributive property allows us to factor out common terms from groups of terms in a polynomial.

Front

What is the role of coefficients in polynomial factoring?

Back

Coefficients are the numerical factors in front of the variables in a polynomial, and they can affect the grouping and factoring process.

Front

Can all polynomials be factored?

Back

Not all polynomials can be factored over the integers; some are prime polynomials.

Front

What is a prime polynomial?

Back

A prime polynomial is a polynomial that cannot be factored into the product of two non-constant polynomials.