How do you factor $5d^2-4d-1$ ?

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Answer 1 · 2016-05-08T17:18:28

$color(blue)( (5d +1 ) ( d - 1 )$ is the factorised form of the expression.

$5d^2 -4d - 1$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ad^2 + bd + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 5* (- 1) = -5$

AND

$N_1 +N_2 = b = -4$

After trying out a few numbers we get $N_1 = -5$ and $N_2 =1$
$(-5)*(1) = -5$ , and $1 +(-5)= -4$

$5d^2 -4d - 1 =5d^2 -5d + 1d - 1$

$=5d ( d - 1 )+ 1 (d - 1)$

$(d-1)$ is a common factor to each of the terms:

$= color(blue)( (5d +1 ) ( d - 1 )$

How do you factor 5d^2-4d-15d^2-4d-1?