Question

Factor 2x^2-10x+8 completely

Answer 1

2(x^2-5x+4) That's the smallest I see. Double check though. I might be misunderstanding the way it ways the answer.

Answer 2

Answer:

2(x-1)(x-4)

Step-by-step explanation:

You can see immediately that 2 is a factor of each term. That lets you write ...

... = 2(x² -5x +4)

To factor further, you need factors of 4 that add to -5. Those would be -1 and -4. Now, you can write ...

... = 2(x -1)(x -4)

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Comment on this factorization

It is not uncommon to see quadratics in which the constant is 1 less than the magnitude of the linear term. (4 is 1 less than 5 in this case) Then the constant term and 1 are the constants in the binomial factors. Signs need to be appropriate, of course.

Another way to say this is that when the sum of all the coefficients of the polynomial is zero, 1 is a root and (x -1) is a factor.