Question

Without actual division , prove that (2x)4-(6x)3+(3x)2+3x-2 is exactly divisible by x2-3x+2.

Answer 1

Hey mate here's your answer hope it will help you

Answer 2

Step-by-step explanation:

Suppose f(x) = 2x^4 - 6x^3 + 3x^2 + 3x - 2

Suppose g(x) = (x^2 - 3x + 2) = x^2 - 2x - x + 2

= x(x - 2) - (x - 2) = (x - 2)(x - 1)

f(x) will be divisible by g(x) if exactly divisible by (x - 2) and (x - 1)

f(2) = 0 and f(1) = 0

f(2) = $\bf\huge 2\times 2^4 - 6\times 2^3 + 3\times 2^2 + 3\times 2 - 2$

⇒ 32 - 48 + 12 + 6 - 2 = 0

 

Hence Proved