Question

Draw the element of the given polynomial.

(y+2)(y-3)(y+8)(y+3)+56​

Answer 1

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️ ( y²+5y-22 ) ( y+4 ) ( y+1 )

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= ( y+2 ) ( y+3 ) ( y-3 ) ( y+8 ) +56

= [( y²+3y+2y+6 )] [( y²+8y-3y-24 )] +56

= ( y²+5y+6 ) ( y²+5y-24 ) +56

Now

Consider y² + 5y = m,

( m+6 ) ( m-24 ) +56

= m²-24m + 6m-144+56

= m²-22m + 4m-88

= m( m-22 ) + 4( m-22)

= ( m-22 ) ( m+4 )

"Now consider y² + 5y In place of m"

( y²+5y-22 ) ( y²+5y+4 )

= ( y²+5y-22 ) ( y²+4y+y+4 )

= ( y²+5y-22 ) [y(y+4) + 1( y+4 )]

=( y²+5y-22 ) ( y+4 ) ( y+1 )

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