Question

The Expression 4x^2-p(x)+7 leaves a remainder of -2 when divided by (x-3) find the value of p

Answer 1

Answer:

(c)  For p = 15,  $4x^2-p(x)+7$ leaves a remainder of -2 when divided by (x-3).

Step-by-step explanation:

Here,  The dividend expression is  $4x^2-p(x)+7$ = E(x)

The Divisor = (x-3)

Remainder  = -2

Now, by REMAINDER THEOREM:

Dividend  = (Divisor x Quotient)  + Remainder

If ( x -3 ) divides the given polynomial with a remainder -2.

⇒  x = 3  is a  solution of given polynomial E(x)  - (-2) =  

$E(x) - (-2) = 4x^2-p(x)+7 -(-2) = 4x^2-p(x)+9$ =  S(x)

Now, S(3) = 0

⇒$4x^2-p(x)+9 = 4(3)^2 - p(3) + 9 = 0\\\implies 36 - 3p + 9 = 0\\\implies 45= 3p , \\or p =15$

or, p =1 5

Hence, for p = 15,  $4x^2-p(x)+7$ leaves a remainder of -2 when divided by (x-3).