Question

Factorise 2x⁴+x³-14x²-19x-6

Answer 1

@
2x⁴+x³-14x²-19x-6
Putting x=3
p(3)=2(3)⁴+(3)³-14(3)²-19(3)-6
=>0
(x-3) is a factor
__________________
Dividing 2x⁴+x³-14x²-19x-6 by x-3

x-3) 2x⁴+x³-14x²-19x-6( 2x³+7x²+7x+2
-2x⁴+6x³
______
7x³-14x²
-7x³+21x²
_______
7x²-19x
-7x²+21x
_______
2x-6
-2x+6
_______
00
=>2x³+7x²+7x+2
≈≈≈×≈≈≈≈≈×
2x⁴+x³-14x²-19x-6
=>(x-3)(2x³+7x²+7x+2)
=>(x-3){2(x³+1)+7x(x+1)}
=>(x-3)(2+7x)(x³+x+2)
@:-)