Question

Find the value of 'a' for which (x-3) is a factor of x3+x into 2 -17 x+a​

Answer 1

Answer:

The value of a is 18.

Step-by-step-explanation:

The given polynomial is x³ + 2x - 17x + a.

Let the polynomial be P ( x ).

We have given that,

( x - 3 ) is a factor of the given polynomial.

By factor theorem,

If x = 3, P ( x ) = 0

∴ ( 3 )³ + 2 * 3 - 17 * 3 + a = 0

⇒ 27 + 6 - 51 + a = 0

⇒ 33 - 51 + a = 0

⇒ a - 18 = 0

⇒ a = 18

∴ The value of a is 18.

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Additional Information:

Factor theorem:

If P ( x ) is a polynomial in variable x and P ( x ) equals to 0 for x = a, then ( x - a ) is a factor of P ( x ).

And if ( x - a ) is a factor of polynomial P ( x ), then x = a is root of P ( x ) i. e. when x is equal to a, P ( x ) is equal to 0.