Question

Prove that 2x4 – 6x3 + 3x2 + 3x – 2 is exactly divisible by x2 – 3x +2

i. By actual division​

Answer 1

-6

8-18+6+3*0-2

*2-3*0+2

Answer 2

you can solve by splitting middle term for x²-3x+2 will be (x-1) , (x-2)......(i) now

you can solve by splitting middle term for x²-3x+2 will be (x-1) , (x-2)......(i) now p(x)=2x⁴-6x³+3x²+3x-2

you can solve by splitting middle term for x²-3x+2 will be (x-1) , (x-2)......(i) now p(x)=2x⁴-6x³+3x²+3x-2now put the value of x=1,2. [from (i)]

you can solve by splitting middle term for x²-3x+2 will be (x-1) , (x-2)......(i) now p(x)=2x⁴-6x³+3x²+3x-2now put the value of x=1,2. [from (i)]p(1)=2(1)⁴-6(1)³+3(1)²+3(1)-2 =>0also, p(2)=2(2)⁴-6(2)³+3(2)²+3(2)-2 =>0this conclude that x²-3x+2 is divisible by 2x⁴-6x³+3x²+3x-2:•hence proved