Kayla H.

asked • 03/05/21

For the following problem both factors should be (2x - 5), What specifically tells you that both those factors should have a minus sign? *

16x²-80x+100

4(4x²-20x+25)

4(2x-5)(2x+5)

Brenda D.

tutor
In order for the sign on the constant to be positive you must have factors that multiply to give a positive; (negative*negative=positive) and (positive*positive= positive) and sum to give a negative middle term both options must be met. (-5*-5= 25) and (-10x - 10x = -20x). You can also check the last option to find that (2x-5)(2x+5) when multiplied will cancel out the middle term. (2x-5)(2x+5) are the factos for the difference between two perfect squares and will multiply to 4x^2 - 25.
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03/06/21

1 Expert Answer

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Paul M. answered • 03/05/21

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BS Mathematics, MD
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The factors should NOT have a minus sign; they should be positive.

But the sign in the middle of the binomial should be negative

The minus sign on the x term and the + sign on the constant term mean the the sign in the middle of the 2 binomial factors must be minus.

I'm not sure how to comment on the last one, except that the product will have a negative sign on the constant term.

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