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Factor 20c²+43c+14.

a) (4c+7)(5c+2)

b) (5c+2)(4c+7)

c) (2c+5)(7c+4)

d) (7c+4)(2c+5)

1 Answer

3 votes

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.

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