`p(x) = 4x^3+ax^2+9x+9`

It is given that when p(x) is divided by (2x-1) then the remainder is 10

Using remainder theorem;

`p(1/2)=10`

`4(1/2)^3+a(1/2)^2+9(1/2)+9=10`

`1/2+a/4+9/2+9=10`

`a/4+14=10`

`a=-16`

**So the value of a=-16**

The remainder when p(x) is divided by (x-3) is given by p(3).

`p(3) = 4(3)^3+a(3)^2+9 xx 3 + 19`

`=27 xx 4 – 16 xx 9 + 27 + 9`

`=144-144`

`=0`

*Since the remainder is 0, (x-3) is a factor of p(x)*

**Further Reading**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now