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

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

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

Step-by-step explanation:

The red lines signify congruency. Meaning, if one angle (say <EFD) is 75 and has one red line and <JAB also has one red line, it means it also equals 75.
Just like <GHF is 130 and has two lines, <JBC also has two red lines, so it also equals 130.