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The polynomial ax^3–3x^2−11x + b, where a and b are constants, is denoted by p(x)....

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saj-94 | Salutatorian

Posted September 24, 2013 at 6:02 PM via web

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The polynomial ax^3–3x^2−11x + b, where a and b are constants, is denoted by p(x). It is given that (x + 2) is a factor of p(x), and that when p(x) is divided by (x + 1) the remainder is 12.

Find the values of a and b.

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aruv | High School Teacher | Valedictorian

Posted September 24, 2013 at 6:15 PM (Answer #1)

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`P(x)=ax^3-3x^2-11x+b`

`(x+2) is ` factor of P(x)

`=>P(-2)=0`

`-8a-12+22+b=0`

-8a+10+b=0     (i)

Also when (x+1) divides P(x) ,remainder is 12

This implies

P(-1)=12

-a-3+11+b=12

-a-4+b=0        (ii)

subtract (ii) from (i)

-7a+14=0

-7a=-14

a=2

substitute a in (ii)

-2-4+b=0

b=6

Thus

a=2 and b=6

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