Question

2. If the quotient on dividing then find a, b and also the remainder.

Answer 1

x⁴ + 10x³ + 35x² + 50x + 29 by (x + 4) is x³ - ax² + bx + 6
$\bold{\frac{x^4+10x^3+35x^2+50x+29}{x+4}=x^3-ax^2+bx+6}$

x + 4) x⁴ + 10x³ + 35x² + 50x + 29 ( x³ + 6x² + 11x + 6
x⁴ + 4x³
________
6x³ + 35x²
6x³ + 24x²
__________
11x² + 50x
11x² + 44x
____________
6x + 29
6x + 24
__________
+5

Hence, remainder is 5
Now, compare x³ + 6x² + 11x + 6 with x³ - ax² + bx + 6
then, we get a = -6 and b = 11

Hence, a = -6 and b = 11
And remainder = 5

Answer 2

Solution :

Let p(x) = x⁴+10x³+35x²+50x+29 ,

g(x)= x + 4 ,

q(x) = x³ - ax² + bx + 6 ,

******************"**********************
Division Algorithm :

Dividend=divisor×quotient+ remainder
***************************************
x³+6x²+11x+6
________________
x+4|x⁴+10x³+35x²+50x+29|
*****x⁴+4x³
_______________
********6x³+35x²
********6x³+24x²
_______________
*************11x²+50x
*************11x²+44x
_______________
*******************6x+29
*******************6x+24
___________________
*************************( 5 )

Compare given q(x ) with

x³ + 6x²+11x+6 we get

a = -6 , b = 11 ,

Remainder = 5

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