Factor by Grouping

Front

What is Factor by Grouping?

Back

A method used to factor polynomials by grouping terms with common factors.

Front

What is the first step in Factor by Grouping?

Back

Group the terms of the polynomial into pairs or sets that have common factors.

Front

How do you factor the expression 7r³ - 8r² + 42r - 48?

Back

(r² + 6)(7r - 8) after grouping and factoring.

Front

What is a common factor?

Back

A number or expression that divides two or more numbers or expressions evenly.

Front

What is the purpose of factoring polynomials?

Back

To simplify expressions, solve equations, and find roots.

Front

How do you check if your factorization is correct?

Back

Multiply the factors back together to see if you obtain the original polynomial.

Front

What is the result of factoring 20x³ - 25x² + 4x - 5?

Back

(5x² + 1)(4x - 5) after grouping and factoring.

Front

What is the significance of the coefficients in a polynomial?

Back

Coefficients are the numerical factors that multiply the variable terms in a polynomial.

Front

What does it mean to factor completely?

Back

To break down a polynomial into its simplest factors that cannot be factored further.

Front

What is the expression for factoring x³ - 5x² + 5x - 25?

Back

(x² + 5)(x - 5) after grouping and factoring.