Factor each trinomial, if possible. See Examples 3 and 4. 8h²-2h-21

Verified step by step guidance

1. Identify the trinomial to factor: \$8h^2 - 2h - 21$.
2. Multiply the coefficient of \(h^2\) (which is 8) by the constant term (which is -21) to get \(8 \times (-21) = -168\).
3. Find two numbers that multiply to \(-168\) and add up to the middle coefficient, which is \(-2\).
4. Rewrite the middle term \(-2h\) as the sum of two terms using the two numbers found in the previous step, splitting the middle term accordingly.
5. Group the terms in pairs and factor out the greatest common factor (GCF) from each group, then factor out the common binomial factor to complete the factoring process.

Key Concepts

Factoring Trinomials

Factoring trinomials involves expressing a quadratic expression of the form ax^2 + bx + c as a product of two binomials. This process simplifies the expression and helps solve equations or analyze functions. Recognizing patterns and using methods like trial and error or grouping are common approaches.

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest factor shared by all terms in an expression. Identifying and factoring out the GCF first simplifies the trinomial, making further factoring easier. For example, factoring out 2 from 8h^2 - 2h - 21 simplifies the coefficients before applying other methods.

Factoring by Grouping

Factoring by grouping is a technique used when the leading coefficient is not 1. It involves splitting the middle term into two terms whose coefficients multiply to the product of the leading coefficient and the constant term. Then, grouping terms and factoring each group helps factor the entire trinomial.