Question

what number must be added to 2 x cube minus 7 x square + 2 X so that the resulting polynomial sleeves the remains -2 when divided by 2 x minus 3​

Answer 1

Let

$\bold{f(x)=2x^3 –7x^2 +2x }$

And p must be added to f(x)

$\bold{∴f' (x)=2x^3 –7x^2 +2x+p}$

Dividing f(x) by 2x−3 by long division method, we get

$\small \bold{2x^3 –7x^2 +2x+p=(2x−3)(x^2 −2x−2)+(p−6)}$

Hence, remainder is p–6

⇒p−6=−2[given, remainder =−2]

⇒p=−2+6

⇒p=4

Therefore, 4 is to be added.