Question

without actual division prove that 2x4-8x3+3x2+12x-9 is exactly divisible by x2-4x+3​

Answer 1

Answer:

It is exactly divisible.

Step-by-step explanation:

let f(x) = 2x^4 - 8x^3 +3x^2 +12-9

if f(x) is exactly divisible by x^2 4x +3 =

(x-1) (x-3) then f(1)-0 and f(3)=0

thus,

f(1)= 2(14 8(13 3(1r2 +12(1) -9

2-8 +3 +12-9

=0

and,

f(3)=2(3 4-8(33 +3(32 +12(3)-9

=162 216 +27+36 -9

=0

hence f(x) is exactly divisible by x^2 - 4x

+3