Question

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

Answer 1

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)

Answer 2

(x +13)(x + 2)

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)