Question

Replace y by I inpu
2
2
2
2
=0
So, (2y+1) is a factor of ply). That is ply) is a multiple of (2y+1).
Example-11. If the polynomials or +37-13 and 2x - 5x + a are divided
the same remainder, find the value of a.
23​

Answer 1

Answer:

Given p(y)=4y

3

+4y

2

−y−1 is a multiply of (2y+1)

To check that 2y+1 is the factor the value of 2y+1=0 so y=−

2

1

So put y=−

2

1

in expression we get

p(−

2

1

)=4(−

2

1

)

3

+4(−

2

1

)

2

−(−

2

1

)−1

⇒p(−

2

1

)=4×−

8

1

+4×

4

1

−

2

1

−1

⇒p(−

2

1

)=

2

1

+1−

2

1

−1

⇒p(−

2

1

)=0

So remainder is zero when 2y-1 divided polynomial 4y

3

+4y

2

−y−1

Then 2y+1 is a multiple or factor of polynomial 4y

3

+4y

2

−y−1