Question

factories- 2x^2-17x-84 give the right answer no scam​

Answer 1

$\sf\pink{ 2{x}^{2} - 17x - 84}$

First we will find the factors of the constant (84 × 2) = 168. And then find if their sum or difference gives us 17 .

168

/ \

2 x 84 (84+2 is not =17) (84-2 is not = 17)

Hence this pair isn't helpful

168

/ \

3 × 56 (56+3 is not = 17) (56-3 is not = 17)

Hence this pair isn't helpful

168

/ \

4 × 42 (42+4 is not = 17) (42 - 4 is not = 17)

Hence this pair isn't helpful

168

/ \

6 × 28 (28+6 is not = 17) (28 - 6 is not = 17)

Hence this pair isn't helpful

168

/ \

7 × 24 (24+7 is not = 17) $\sf\pink{(24 - 7 = 17)}$

So, this pair is helpful

So here we have got :

24 × 7 = 168

24 - 7 = 17

Hence we have split the middle term.

$\longrightarrow{\sf\green{ 2{x}^{2} - 24x - 7x - 84}}$

$\implies{\sf\green{ 2x(x - 12) - 7(x - 12)}}$

So , the factorization is :

( 2x - 7 ) ( x - 12)