Question

Check whether (y+2) is a factor of 4 + 3 −
^2 + 5
^3

​

Answer 1

Step-by-step explanation:

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

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