Question

Hello people ~
factorise: x^2 + 15x + 26​

Answer 1

Answer:

(x +13)(x + 2)

Step-by-step explanation:

Sum = 15

Product = 26

Factors = 2 , 13

When we add the factors , we get 15 ( 13 +2 = 15)

When we multiply 2 and 13, we get 26 (13*2 = 26)

x² + 15x + 26 = x² + 13x +2x  + 26

                     =x(x + 13) + 2(x + 13)

                      = (x +13)(x + 2)

Answer 2

So far as to attempt this question we can do either it by factorisation method by creating factors OR by splitting middle term method.

$\mapsto\sf{ {x}^{2} + 15x + 26}$

Splitting middle term 15x in terms of 13x and 2x gives their sum to 15x and their product is equal to 26.

$\mapsto\sf{ {x}^{2} + 13x + 2x + 26 = 0}$

$\mapsto\sf{x(x + 13) + 2(x + 13)} = 0$

$\mapsto\sf{(x + 2)(x + 13) = 0}$

CASE 1:

$\mapsto\sf{x + 2 = 0}$

CASE 2:

$\mapsto\sf{x + 13 = 0}$

Thus,

$\sf{ \therefore \: ( {x}^{2} + 15x + 26) = (x + 2)(x + 13)}$

PS: (Factorisation method is been resolved in attachment)