Question

find the value of p for which (x-1 ) is a factor of x³+10x²+px​

Answer 1

Answer:

The value of p is - 11.

Step-by-step-explanation:

The given polynomial is x³ + 10x² + px.

Let the polynomial be P ( x ).

We have given that,

( x - 1 ) is a factor of the given polynomial.

By factor theorem,

If x = 1, P ( x ) = 0

∴ ( 1 )³ + 10 * ( 1 )² + p * 1 = 0

⇒ 1 + 10 * 1 + p = 0

⇒ 1 + 10 + p = 0

⇒ 11 + p = 0

⇒ p = - 11

∴ The value of p is - 11.

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Verification:

The given polynomial is x³ + 10x² + px.

We have, p = - 11.

By substituting p = - 11 in polynomial,

P ( x ) = x³ + 10x² - 11x

⇒ P ( x ) = x ( x² + 10x - 11 )

⇒ P ( x ) = x ( x² - x + 11x - 11 )

⇒ P ( x ) = x [ x ( x - 1 ) + 11 ( x - 1 ) ]

⇒ P ( x ) = x [ ( x - 1 ) ( x + 11 ) ]

⇒ P ( x ) = x ( x - 1 ) ( x + 11 )

( x - 1 ) is a factor of the polynomial x³ + 10x² + px when p = - 11.

Hence verified!