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

검증된 단계별 안내

Identify the trinomial to factor: $14m^2 + 11mr - 15r^2$.

Multiply the coefficient of $m^2$ (which is 14) by the coefficient of $r^2$ (which is -15), giving $14 \times (-15) = -210$.

Find two numbers that multiply to $-210$ and add up to the middle coefficient, 11.

Rewrite the middle term \$11mr$ as the sum of two terms using the two numbers found, splitting $11mr$ into two terms with $m$ and $r$.

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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