Question

factorise x3+4x2-7x+10

Answer 1

x^3-4x^2-7x+10
let x=1
(1)^3-4(1)^2-7(1)+10
1-4-7+10=0
so, (x-1) is a factor.
now divide x^3-4x^2-7x-10 from (x-1)=x^2-3x-10
then by spliting the middle term
x^2-3x-10
x^2-5x+2x-10
x(x-5)+2(x-5)
(x+2)(x-5)
factors are (x-1) (x+2) (x-5)
hope it will help u

Answer 2

x³−4x²−7x+10

⇒x³ + x² -2x - 5x² -5x + 10

⇒ x ( x² +x -2) -5 ( x² + x - 2)

⇒( x-5) ( x² + x - 2)    [ by splitting the middle term ]

⇒ ( x-5) ( x² + 2x - x  -2)

⇒ ( x -5 ) { x ( x+2) - 1 ( x +2)}

⇒ ( x-5) ( x-1) ( x+2)

Hence the solution will be  ( x-5) ( x-1) ( x+2).

Ans :-  The solution will be  ( x-5) ( x-1) ( x+2).

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