Question

Factorise: 5m2 – 10 m – 240.

Answer 1

Answer:

(5m ^ 2 - 10m - 240) = (5 (m² - 2m - 48))

To factor the quadratic function

m ^ 2 - 2m - 48 ,

we should solve the corresponding quadratic equation

m ^ 2 - 2m - 48 = 0

Indeed,

if m₁ and m2 are the roots of the quadratic equation

a * m ^ 2 + bm + c = 0 ,

then a * m ^ 2 + bm + c = a(m — m₁)(m – m₂) -

Solve the quadratic equation

Solve the quadratic equation m ^ 2 - 2m - 48 = 0 .

Solve the quadratic equation m ^ 2 - 2m - 48 = 0 .The roots are m_{1} = 8 , m_{2} = - 6

Therefore,

m ^ 2 - 2m - 48

= (m − 8) (m + 6)

=>

5(m ^ 2 - 2m - 48)

= 5 [(m-8) (m + 6)]

Thus,

5m^2−10m−240 = 5[(m−8)(m+6)].

Answer 2

5(m(m+6)-(8m+6)

5(m-8)(m-6)