Question

The polynomial ax cube minus 3x square +4 and 2x cube minus 5x+a wgen divided by (x minus 2) leave the remainder when divided by (x mnus 3) find the value

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ!

( x - 2 ) is factor of ax³ - 3x² + 4
So, x = 2

p(x) = a(2)³ - 3(2)² + 4
p(x) = 8a - 8 ______(1)

( x - 3 ) is factor of p(x)
So, x = 3

p(x) = 2x³ - 5x + a
p(x) = 2(3)³ - 5(2) + a
p(x) = 44 + a _______(2)

As, in both equations p(x) i.e., LHS is same so;

8a - 8 = 44 + a
8a - a = 44 + 8
7a = 14 => a = 52 / 7 or 7.4

But, if you mean to common factor ( x - 2 ) and not ( x - 3 ) and typed wrong then,

p(x) = 2(2)³ - 5(2) + a
p(x) = 6 + a

8a - 8 = 6 + a
7a = 14
a = 14 / 7 or 2 ( which is answet in most of books )

So, choose solution according to your question.

Hope it helps