Question

2 x square - 13 x minus 34 solved using middle term splitting technique

Answer 1

2x2-13x-34  

first we will multiply 2 and 34.then, we will take all the factors of 34*2 =68 and see that if the any when subtracted or added equal to the mid term 13

so the factors of 68 are,

1*68

2*34

4*17

so here we see that 17x-4x is equal to 13x but we need -13x so we will take -17x+4x.

the equation will be

2x2-17x+4x-34

now we will arrange them in pairs so that we get a good and easy factorizing.

2x2+4x-17x-34

then we will take 2x common from first and second term and -17 from other as to make x+2 common.

2x(x+2)-17(x+2)

the here we can see x+2 as common in both of them.

so we will do as follows

(x+2)(2x-17)

if you have any doubt regarding taking common please resolve it to know that it is correct.

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Answer 2

$\large{\boxed{\boxed{\boxed{\bold{\red{Solution : \longrightarrow}}}}}}$

$\blue{= {2x}^{2} - x(17 - 4) - 34 }\\ \\ \blue{= {2x}^{2} - 17x + 4x - 34} \\ \\ \blue{= x(2x - 17) + 2(2x - 17) }\\ \\ \blue{= (2x - 17)(x + 2)}$