Question

if x^5+2x^4+35 is divided by x-1 find the remainder

Answer 1

the answer is 38

#Hassan

Answer 2

2 methods - first is long division by (x+2)

(x+2),2nd is to us remainder theorem

let f(x)=4x2+2kx-5

f(x)=4x2kx-5

And g(x)=x+2

g

(

x

)

=

x

+

2

to find the remainder of f(x)g(x)

f

(

x

)

g

(

x

)

where g(x)=(x+c)

g

(

x

)

=

(

x

+

c

)

we need to evaluate f(−c)

f

(

−

c

)

f(−2)=4(−2)2+2k(−2)−5

f

(

−

2

)

=

4

(

−

2

)

2

+

2

k

(

−

2

)

−

5

Because the remainder is 3, we know that f(−2)=3

f

(

−

2

)

=

3

so

16−4k−5=3

16

−

4

k

−

5

=

3

4k=8

4

k

=

8

k=2

k

=

2

is that correct?