How do you factor the trinomial $6x^2-11x+3$ ?

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Answer 1 · 2016-05-14T07:01:38

$color(green)( (3x - 1 ) ( 2x - 3 )$ is the factorised form of the expression.

$6x^2 - 11x + 3$

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

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

$N_1*N_2 = a*c = 6*3 = 18$

AND

$N_1 +N_2 = b = -11$

After trying out a few numbers we get $N_1 = -9$ and $N_2 =-2$

$( - 9 ) * ( - 2 ) = 18$ , and $(- 9) + ( - 2 )= -11$

$6x^2 - 11x + 3 = 6x^2 - 9x - 2x + 3$

$= 3x( 2x - 3 ) - 1(2x - 3 )$

$(2x - 3 )$ is a common factor to each of the terms

$=color(green)( (3x - 1 ) ( 2x - 3 )$

How do you factor the trinomial 6x^2-11x+36x^2-11x+3?