Question

By actual division show that x2-3 is a factor of 2x4 +3x3 -2x3 -9x-12.

Answer 1

Answer:

(x²-3) is a factor of 2x⁴+3x³-2x²-9x-12.

Step-by-step explanation:

Let p(x)=2x⁴+3x³-2x²-9x-12,

and g(x)=x²-3.

Find p(x)÷g(x)

Quotient:2x²+3x+4

x²-3)2x⁴+3x³-2x²-9x-12(

***** 2x⁴+0-6x²

_______________________

********* 3x³+4x²-9x

********* 3x³+0 -9x

________________________

************* 4x²-12

************* 4x²-12

_________________________

Remainder (0)

Therefore,

g(x) is a factor of p(x)

(x²-3) is a factor of 2x⁴+3x³-2x²-9x-12.

•••♪

Answer 2

Answer:

Step-by-step explanation:

(x²-3) is a factor of 2x⁴+3x³-2x²-9x-12.

Step-by-step explanation:

Let p(x)=2x⁴+3x³-2x²-9x-12,

and g(x)=x²-3.

Find p(x)÷g(x)

Quotient:2x²+3x+4

x²-3)2x⁴+3x³-2x²-9x-12(

***** 2x⁴+0-6x²

_______________________

********* 3x³+4x²-9x

********* 3x³+0 -9x

________________________

************* 4x²-12

************* 4x²-12

_________________________

Remainder (0)

Therefore,

g(x) is a factor of p(x)

(x²-3) is a factor of 2x⁴+3x³-2x²-9x-12.