Question

How do you factor `2x^2 -7x -15`?

Answer 1

`(x-5)(2x+3)`

Thought processes explained!

Explanation:

Whole number factor of 2 can only be {2 , 1}

Whole number factors of 15 are {1 , 15}; {3 , 5}
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Lets experiment!

We know that we have to start with: `(1x+?)(2x+?)`
Which when written as per convention is `(x+?)(2x+?)`

We know that `2xx15=30` which is a long way from the 7 in `7x` so we will not use that to start with

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Try this:

`(x+3)(2x+5) = 2x^2+5x+6x+15 " "color(red)("Fail!")`
For a start we have +15 and we need -15. Also the 7 from `7x` is -7. So the larger of the two gas to be negative.

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Try this:

`(x+3)(2x-5) = 2x^2-5x+3x-15 " "color(red)("Fail. This gives -2x")`

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Try swapping the 3 and 5 around

`(x-5)(2x+3) = 2x^2+3x-10x-15 " "color(green)("Works!")`

`2x^2+3x-10x-15" "=" "2x^2-7x-15`