When factoring 3x^2 - 26x + 35, why should both factors of c be negative

Question

Mathematics

Cindy Lou Who

15 October, 20:32

When factoring 3x^2 - 26x + 35, why should both factors of c be negative

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Hudson Hartman · Answer 1

So you want to factor this polynom thus it will look like something like this

(x+a) (x+b) where a and b can be positive or negative

now in our question the polynom ends with + 35 that has no x in it. This part can only come from a*b. Two numbers multiplied can only be positive if they are both positive or if they are both negative.

-26x this part comes from ax+bx part of the above equation. If both a and b are poitive than the result needs to be positive as well, this combining the two arguements we come to the conclusion that they are both negative.