Using factor theorem, factorise 2y3-5y2-19y+42
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2y cube -5y sq. -19y+2
by using synthetic division
= 2[2 -5 -19 +42]
--->[0 4 -2 -42]
---------------------------
---->2 -1 -21 00
i.e. = (x-2)(2x sq. -x -21)
= (2x sq +6x -7x - 21)(x-2)
=[ 2x(x+3)-7(x+3) ](x-2)
=(2x-7)(x+3)(x-2)
:. 2x-7=0 or x+3=0 or x-2=0
:. x=7/2 or x= -3 or x=2
by using synthetic division
= 2[2 -5 -19 +42]
--->[0 4 -2 -42]
---------------------------
---->2 -1 -21 00
i.e. = (x-2)(2x sq. -x -21)
= (2x sq +6x -7x - 21)(x-2)
=[ 2x(x+3)-7(x+3) ](x-2)
=(2x-7)(x+3)(x-2)
:. 2x-7=0 or x+3=0 or x-2=0
:. x=7/2 or x= -3 or x=2
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