How do you factor the trinomial $6 x^{2} - 5 x - 25$ $6x^2 - 5x - 25$ ?

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Answer 1 · 2016-05-26T15:30:29

$(3 x + 5) (2 x - 5)$ $color(blue)( (3x + 5 ) ( 2x - 5)$ is the factorised form of the expression.

$6 x^{2} - 5 x - 25$ $6x^2 -5x -25$

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

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

$N_{1} \cdot N_{2} = a \cdot c = 6 \cdot (- 25) = - 150$ $N_1*N_2 = a*c = 6*(-25) = -150$

AND

$N_{1} + N_{2} = b = - 5$ $N_1 +N_2 = b = -5$

After trying out a few numbers we get $N_{1} = - 15$ $N_1 = -15$ and $N_{2} = 10$ $N_2 =10$

$10 \cdot (- 15) = - 150$ $10* (-15) = -150$ , and $10 + (- 15) = - 5$ $10+(-15)= -5$

$6 x^{2} - 5 x - 25 = 6 x^{2} - 15 x + 10 x - 25$ $6x^2 -5x -25 = 6x^2 -15 x + 10x -25$

$= 3 x (2 x - 5) + 5 (2 x - 5)$ $= 3x ( 2x - 5) + 5 (2x -5)$

$(2 x - 5)$ $(2x-5)$ is a common factor to each of the terms:

$= (3 x + 5) (2 x - 5)$ $=color(blue)( (3x + 5 ) ( 2x - 5)$

How do you factor the trinomial 6x2−5x−256x^2 - 5x - 25?