Question

x3_10x2-53x-42 factorise it using factor theorem

Answer 1

let p(x)=x^3-10x^2-53x-42
here,-42=+ or- 1×42
+ or- 2×21
+ or- 3×14
now, let's check by (x+3)or (x-3) we get 0
with x+3
x=-3
here, p(-3)=(-3)^3-10 (-3)^2-53(-3)-42
= -27-90+159-42
= -27+69-42
= -27+27
=0
therefore (x+3) is the factor

now dividing x^3-10x^2-53x-42 by the factor x+3 we get:
division is in the above pic
now
p (x)=x^2-13x-14
=x^2-14x+1x-14 [by splitting the middle
=x (x-14)+1 (x-14) term]
=(x+1)(x-14)(x+3)

Answer 2

Answer:

(x+1)(x-14)(x-3)

Step-by-step explanation: