Factorise: x^2 - 16 + 6x - 24?

x² - 16 + 6x - 24 = 0

Collect like terms

x² + 6x - 40 = 0

The middle term is + 6x

The first term x² = 1

Find the sum of the middle term

Multiply the first term 1 times the last term 40 equals 40 and factor

Factors of 40

1 x 40
2 x 20
4 x 10. . .←. .use these factors
8 x 5

+ 10x and - 4x satisfy the sum of the millde term

Insert + 10x and - 4x into the equation

x² + 6x - 40 = 0

x² + 10x - 40x - 40 = 0

Group factor

(x² + 10x) - (4x - 40) = 0

Greatest common factor (GFC)

x(x + 10) - 4(x + 10) = 0

(x - 4)(x + 10) = 0
- - - - - - - - - -

Roots

x - 4 = 0

Transpose 4

x - 4 + 4 = 0 + 4

x = 4

Insert the x value into the equation.
- - - - - - - -

Roots

x + 10 = 0

Transpose 10

x + 10 - 10 = 0 - 10

x = - 10

Insert the x value into the equation
- - - - - - - - -

Check for zero (0)

x+ 4

x² + 6x - 40 = 0

(4)² + 6(4) = 0

16 + 24 - 40 = 0

Working left to right

40 - 40 = 0

0 = 0
- - - - - - - -

Check for zero )0)

x - 10

x² + 6x - 40 = 0

(- 10)² + 6(- 10) - 40 = 0

100 + (- 60) - 40 = 0

remove parenthesis

100 - 60 - 40 = 0

Working left to right

40 - 40 = 0

0 = 0
- - - - - - - - -

The solujtion for equation x² + 6x - 40 = 0

are x = 4 and x - 10
- - - - - - - - -s-

x^2-16+6x-24
=x^2+6x-40
=x^2+10x-4x-40 (as 10+-4=6 and 10x-4=-40)
=x(x+10)-4(x+10)
=(x+10)(x-4)

[1]
x^2-16+6x-24
=(x^2-16)+(6x-24)
={(x)^2-(4)^2}+6(x-4)
=(x+4)(x-4)+6(x-4)
=(x-4)(x+4+6)
=(x-4)(x+10)

x^2 - 16 + 6x - 24
=x^2+6x-40
=(x+10)(x-4)

x^2 - 16 + 6x - 24

Factor the first two terms and the last two terms.

(x + 4)(x - 4) + 6(x - 4)

Note how these two sum of expressions have a factor in common now; (x - 4). Therefore, factor (x - 4) from these two expressions.

(x - 4) (x + 4 + 6)

Which simplifies as

(x - 4)(x + 10)

Collect the terms and get the factors

x^2 - 16 + 6x - 24
x^2 + 6x - 40
(x+10)(x-4)

(x+10)(x-4)

x^2 - 16 + 6x - 24
= x^2 + 6x - 16 - 24
= x^2 + 6x - 40
= (x + 10)(x - 4)