Question

How do you factor the trinomial `8b^2+2b-3`?

Answer 1

`(2b-1)(4b+3)`

Explanation:

Only factors of 3 are {1,3} so this is fixed giving the format of:

`(?+1)(?+3)`.......ignoring the signs

But we have a negative 3 so the signs for the factors need to opposites. One positive and the other negative!

Consider the factors of 8 `-> {1,8}, {2,4}`

So can we end up with 2 in 2b using these?

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`color(blue)("Attempt" color(white)(.) 1)`

`color(brown)((2b+1)(4b-3)color(blue)( = 8b^2 -6b+4b-3) =8b^2-2b-3) color(green)(" Fail")`

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`color(blue)("Attempt" color(white)(.) 2)`

In attempt 1 the 2 in `2b` is negative so we have the correct number but the sign is wrong. Try reversing the signs in the brackets.

`color(brown)((2b-1)(4b+3)color(blue)( = 8b^2-4b+6b-3))`

`color(brown)(=8b^2+2b-3) color(green)(" It works!")`

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