Without actual division, Prove that 2x power four - 6x cube + 3x square + 3x - 2 is exactly divisible by x square - 3x + 2

without division its a little hard but 2 is divisible by any number so ...

Proven below in the explanation

Step-by-step explanation:

Given that:

2x⁴-6x³+3x²+3x-2 ... (1)

x²-3x+2 ... (2)

To proof that equation (1) is exactly divisible by equation (2), substitute an integer for 'x' in the two equations so as to form a whole number.

Assume x = 1

∴For equation (1)

= 2 (1) ⁴-6 (1) ³+3 (1) ²+3 (1) - 2

= 2 - 6 + 3 + 3 - 2

= 0

∴For equation (2)

= (1) ²-3 (1) + 2

= 1 - 3 + 2

= 0

For x = 1, both equations are zero'0'

0/0 = 0