Factor by Grouping and Trinomials

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors together.

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax^2 + bx + c.

Front

How do you factor the trinomial x^2 + 10x + 16?

Back

(x + 2)(x + 8) is the factored form of the trinomial x^2 + 10x + 16.

Front

What is the first step in factoring by grouping?

Back

The first step is to group the terms of the polynomial into pairs that have common factors.

Front

How do you factor the expression 30x^3 + 15x^2 - 18x - 9?

Back

3(5x^2 - 3)(2x + 1) is the factored form of the expression.

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials helps simplify expressions and solve equations more easily.

Front

What is the factored form of x^3 - 5x^2 + 5x - 25?

Back

(x^2 + 5)(x - 5) is the factored form of the expression.

Front

What does it mean to factor out the greatest common factor (GCF)?

Back

Factoring out the GCF means to divide each term of the polynomial by the largest factor that is common to all terms.

Front

How do you factor the expression 2x^3 - 8x^2 - x + 4?

Back

(2x^2 - 1)(x - 4) is the factored form of the expression.

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.