Question

3. If the quotient on dividing, then find p , q and also the remainder.

Answer 1

Final Answer : p = -3 , q = 0 , Remainder = - 10

Steps and Understanding :
1) We will apply Division Algorithm of Polynomials.
Dividend = Divisor * Quotient + Remainder

2) Here,
Dividend =p(x) = 8x^4 -2x^2+6x-7
Divisor = g(x) = 2x+1
Quotient = q(x) = 4x^3 + px^2-qx + 3
Remainder = r(x)

We will apply,
p(x) = q(x) * g(x) + r(x)

3) Then, we will collect all different coefficients of x and compare both sides to get the value of p, q, and r(x).

For Calculation see pic.

Answer 2

Solution :

Let p(x) = 8x⁴-2x²+6x-7 ,

g(x) = 2x + 1 ,

q(x) = 4x³+px²-qx+3 ,

*************************"***************
Divisibility Theorem :

Dividend=divisor×quotient+remainder

******************************************

2x+1| 8x⁴+0-2x²+6x-7|4x³-2x²+3
*******8x⁴+4x³
_______________
*********** -4x³-2x²+6x
***********-4x³ -2x²
_________________
*********************6x-7
*********************6x+3
__________________
********************** ( -4 )

Compare Given q(x) , with

4x³ + 0 - 2x² + 3 ,

we get ,

p = -2 , q = 0 ,

Remainder = -4

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