Home › STAAR EOC Algebra I › Mathematics › Factoring › When factoring 2x^2 + 6x + 5 using the ac method…
When factoring 2x^2 + 6x + 5 using the ac method, what happens after listing the factor pairs of 10?
AThe pair 2 and 5 adds to 6, giving (2x+5)(x+1)
BNo pair adds to 6, so the trinomial is prime
CThe pair 1 and 10 adds to 6, giving (2x+1)(x+5)
DEvery pair adds to 6, giving several valid factorings
Answer & Solution
Correct answer: B. No pair adds to 6, so the trinomial is prime
1. The ac method needs two numbers that multiply to a times c, which is 2 times 5 equals 10, and add to b, which is 6.
2. The factor pairs of 10 are 1 and 10, which add to 11, and 2 and 5, which add to 7.
3. Neither pair adds to 6, so no split of the middle term works and the trinomial 2x squared + 6x + 5 is prime.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1_
Related questions
Factor: x^3 + 64.According to the Sum and Difference of Cubes Pattern, how does a^3+b^3 factor?Factor completely: 36x^2y - 48xy + 16y.Factor completely: 8x^2y - 98y.Factor completely: 6x^2 + 96.What happens when you try to factor a sum of squares like a^2 + b^2?What is the completely factored form of x^4 - y^4?Factor: 100 - h^2.