Question

How do you factor `b^ { 2} - 3b - 4?`

Answer 1

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

Explanation:

The algebraic expression `b^2-3b-4" "`can be factorized using
`" "`
the trial and error method, in other words, the idea is to find two
`" "`
integers `c and d` whose sum `" "color(blue)S = -3" "` and their
`" "`
product is `color(blue)P = -4`
`" "`
Trial and Error Factorization :
`" "`
`X^2+color(blue)SX+color(blue)P =(x+c)(x+d)`

For the expression`" "b^2-3b-4" "`,the two integers satisfying the
`" "`
`color(blue)S` and `color(blue)P` requirements are `c=-4 and d=+1`
`" "`
Therefore,
`" "`
`b^2-3b-4=(b-4)(b+1)`