Question

Factorise : x²+ 15x + 56 .​

Answer 1

`\twoheadrightarrow\quad\sf{(x+7)(x+8)}`

Explanation:

Hi !! Our task is to factorize
`\sf{x^2+15x+56}`.

We will think of two numbers that:

• multiply to 56
• add to 15

These numbers are 7 and 8.

So far, we have:

(x + --- )(x + ---)

The numbers 7 and 8 go in the blanks:

(x + 7)(x + 8

Answer 2

(x + 7)(x + 8)

Explanation:

x² + 15x + 56

consider the factors of the constant term (+ 56) which sum to give the coefficient of the x- term (+ 15)

the factors are + 7 and + 8 , since

+ 7 × + 8 = + 56 and + 7 + 8 = + 15

use these factors to split the x- term

x² + 7x + 8x + 56 ( factor the first/second and third/fourth terms )

= x(x + 7) + 8(x + 7) ← factor out (x + 7) from each term

= (x + 7)(x + 8)