Question

Factorise : 4x^3- 12x² – 15x + 50​

Answer 1

Answer:

Let x=-2

p(x)=4x^3 - 12x^2 - 15x + 50

p(-2) = 4×(-2)^3 - 12 ×(-2)^2 - 15 × -2 + 50

= -32-48+30+50

=-80+80

=0

p(-2)=0

(x+2) is the factor of given polynomial

__________________

x+2 |4x^3 - 12x^2 - 15x + 50 | 4x^2 - 20x + 25

4x^3 + 8x^2

( - ). ( - )

______________

-20x^2 - 15x

-20x^2 - 40x

( + ). ( + )

______________

25x + 50

25x + 50

( - ). ( - )

___________

0

p(x)= (x + 2)(4x^2 - 20x + 25)

=(x+2)[4x^2 -(10+10)x + 25]

=(x+2)[4x^2 - 10x - 10x + 25]

=(x+2)[2x(2x-5) - 5(2x-5)]

=(x+2)(2x-5)(2x-5)