How do you factor the trinomial $24k² + k - 3$ ?

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Answer 1 · 2016-04-25T17:12:27

$color(blue)((8k +3) ( 3k-1 )$ is the factorised form of the expression.

$24k^2 + k - 3$

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

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

$N_1*N_2 = a*c = 24 *(- 3) = -72$

AND

$N_1 +N_2 = b = 1$

After trying out a few numbers we get $N_1 = 9$ and $N_2 =-8$

$9*(-8) = -72$ , and $9+(-8)= 1$

$24k^2 + k - 3 = 24k^2 - 8k + 9k - 3$

$=8k ( 3k-1 ) +3 ( 3k - 1 )$

$(3k-1)$ is a common factor to each of the terms

$= color(blue)((8k +3) ( 3k-1 )$

How do you factor the trinomial 24k² + k - 324k² + k - 3?