Factor each trinomial, if possible. See Examples 3 and 4. 14m²+11mr-15r²

Verified step by step guidance

1. Identify the trinomial to factor: \$14m^2 + 11mr - 15r^2$.
2. Multiply the coefficient of \(m^2\) (which is 14) by the coefficient of \(r^2\) (which is -15), giving \(14 \times (-15) = -210\).
3. Find two numbers that multiply to \(-210\) and add up to the middle coefficient, 11.
4. Rewrite the middle term \$11mr\( as the sum of two terms using the two numbers found, splitting \)11mr\( into two terms with \)m\( and \)r$.
5. Group the four terms into two pairs and factor out the greatest common factor (GCF) from each pair, then factor out the common binomial factor to complete the factoring.

Key Concepts

Factoring Trinomials

Factoring trinomials involves rewriting a quadratic expression as a product of two binomials. For trinomials in the form ax^2 + bx + c, the goal is to find two binomials whose product equals the original trinomial. This process simplifies expressions and solves equations.

Greatest Common Factor (GCF)

Before factoring a trinomial, identify the greatest common factor of all terms. The GCF is the largest expression that divides each term evenly. Factoring out the GCF simplifies the trinomial and makes further factoring easier or possible.

Factoring by Grouping

Factoring by grouping is a method 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 first and last coefficients. Then, group terms and factor each group to find common binomial factors.