Question

find the factors of x³+7x²+8x+2​

Answer 1

Step-by-step explanation:

x³ - 7x² + 11x - 5

Splitting - 7x² in two terms.

- 7x² = - x² - 6x²

x³ - 7x² + 11x - 5

x³ - x² - 6x² + 11x - 5

\begin{gathered} \text{If we notice, we can take} \: x^{2} \text{ common in} \: ( x^{ 3} - x^{2} ) \\ \text{and we can write} - 6x^{2} + 11x - 5 \: \: \text{as} \: \: \bold{ - [ 6x^{2} - 11x + 5 ]}\end{gathered}

If we notice, we can takex

2

common in(x

3

−x

2

)

and we can write−6x

2

+11x−5as−[6x

2

−11x+5]

So,

x²( x - 1 ) - [ 6x² - 11x + 5 ]

Then,

6x² + 11x + 5 is an quadratic equation which can be solved by splitting middle term method. in the equation middle term is 11x, according to the question 11x on splitting, will be 6x + 5x.

x²( x - 1 ) - [ 6x² - 6x - 5x + 5 ]

x²( x - 1 ) - [ 6x( x - 1 ) + 5( x - 1 ) ]

x²( x - 1 ) - ( x - 1 )( 6x + 5 )

( x - 1 )( x² - 6x + 5 )

( x - 1 ) { x² - 5x - x + 5 }

( x - 1 ){ x( x - 5 ) - ( x - 5 ) }

( x - 1 )( x - 1 )( x - 5 )

( x - 5 )( x - 1 )²

Thus,

factors of x^3-7x^2+11x-5 are ( x - 5 ) and ( x - 1 )