Question

By actual division, show that x2 - 3 is a factor of 2x4 + 3x3 - 2x2 - 9x – 12.
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Answer 1

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.

Answer 2

Step-by-step explanation:

Let f(x) = 2x4 + 3x3 – 2x2 – 9x – 12 and g(x) as x2 – 3 Quotient q(x) = 2x2 + 3x + 4 Remainder r(x) = 0 Since, the remainder is 0. Hence, x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12Read more on Sarthaks.com - https://www.sarthaks.com/129312/by-actual-division-show-that-x-2-3-is-a-factor-of-2x-4-3x-3-2x-2-9x-12