Question

(x³+10x²+26x+2) ÷(x+16)​

Answer 1

Let f(x)=x  

3

+10x  

2

−37x+26

Putting x=1, we get

f(1)=1+10−37+26=0

∴ By factor theorem, x−1 is factor of f(x).

On dividing x  

3

+10x  

2

−37x+26 by x−1, we get x  

2

+11x−26 as the quotient and remainder =0.

∴ The other factor of f(x) are the factor of x  

2

+11x−26

Now, x  

2

+11x−26

=x  

2

+13x−2x−26

=x(x+13)−2(x+13)

=(x+13)(x−2)

Hence, x  

3

+10x  

2

−37x+26=(x−1)(x−2)(x+13)

Answer 2

Quotient : x²- 6x + 122

Remainder : -1950