Question

Factor 5x^2 – 10x + 7 completely.

A. (5x + 7)(x – 1)

B. (5x – 5)(x + 2)

C. (5x – 2)(x + 5)

D. prime

Answer 1

the first three answers do not give the given. so is D the correct answer?

Answer 2

I think so but let me check one more time. @RH

Answer 3

ok. thanks

Answer 4

It does not factor over the Reals so D is the answer, as you surmised. @RH

Answer 5

@Directrix can you explain why is prime the answer? I just assumed since the three others don't give the given. But I don't understand why it is prime. Sorry :(

Answer 6

Think about the number "2." It is a prime number because it has exactly two positive factors, itself and 1 over the set of positive integers.

Likewise, 5x^2 – 10x + 7 is prime because it has exactly two factors over the set of Reals, itself and 1.

Answer 7

If the quadratic does not give rise to real factors, then we say that it is prime (divisble by just itself and one over the real field).
The discriminant of this quadratic is negative, hence there are no real factors.

Answer 8

x^2 - 1 is not prime over the set of reals because it has factors of (x + 1) and
(x -1) in addition to itself and 1.

Answer 9

or, there's a discriminant method
if b^2-4ac <0 then its prime .

Answer 10

The discriminant of a quadratic is a means to test whether a quadratic is prime but the nature of the discriminant of a given quadratic is not a definition of a prime quadratic.

Answer 11

Thank you!!!

Answer 12

@RH Glad to help and appreciate your asking questions to ensure your understanding of problems and solutions.