Final answer:
The expression 20c²+43c+14 can be factored into either (4c+7)(5c+2) or (5c+2)(4c+7), as both options expand to the original expression.
Step-by-step explanation:
To factor the quadratic expression 20c²+43c+14, we want to find two binomials that when multiplied together give us the original quadratic expression. We are looking for factors of 20c² and 14 that when multiplied give us 20c² but when added give us the middle term, which is 43c.
Let's analyze the given options:
- Option a: (4c+7)(5c+2) = 20c² + 8c + 35c + 14 = 20c² + 43c + 14
- Option b: (5c+2)(4c+7) = 20c² + 14c + 35c + 14 = 20c² + 43c + 14
- Option c: (2c+5)(7c+4) does not give us the middle term of 43c when expanded
- Option d: (7c+4)(2c+5) does not give us the middle term of 43c when expanded
Both option a and option b are correct as they both expand to the original quadratic expression. However, since they are the same factors in a different order, we can choose either one.