Question

Factorise : x² + 10x + 24 .​

Answer 1

(x + 4)(x + 6)

Explanation:

Hi! Our task is to factorize the expression:

`\sf{x^2+10x+24}`

We think of two numbers that:

• multiply to 24
• add to 10

These are the numbers that multiply to 24:

1 * 24

2 * 12

3 * 8

4 * 6 (these add up to 10!)

Therefore, the factored expression is:

(x + 4)(x + 6)

Answer 2

(x + 4)(x + 6)

Explanation:

x² + 10x + 24

consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term (+ 10)

the factors are + 4 and + 6 , since

+ 4 × + 6 = + 24 and + 4 + 6 = + 10

use these factors to split the x- term

x² + 4x + 6x + 24 ( factor the first/second and third/fourth terms )

= x(x + 4) + 6(x + 4) ← factor out (x + 4) from each term

= (x + 4)(x + 6) ← in factored form