Question

If (x+3) is a factor of polynomial x³+ax²+x+3 than find value of a

Answer 1

Answer:

a = 3

Explanation:

polynomial :- is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variables.

Given that:- (x+3) is a factorial fo x³+ax²+x+3

so, x + 3 = 0 => x = -3

now, by putting the value of x in the polynomial

(-3)³ + a(-3)² + (-3) + 3 = 0

=> -27 + 9a - 3 - 3 = 0

=> 9a - 27 = 0

=> 9a = 27

=> a = 27/9

=> a = 3

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Answer 2

The value of a = 3

Given :

(x + 3) is a factor of polynomial x³ + ax² + x + 3

To find :

The value of a

Concept :

Factor Theorem :

If f(x) be a polynomial then x - a is a factor of f(x) iff f(a) = 0

Solution :

Step 1 of 2 :

Write down the given polynomial

Let f(x) be the given polynomial

Then , f(x) = x³ + ax² + x + 3

Step 2 of 2 :

Find the value of a

Here it is given that (x + 3) is a factor of polynomial x³ + ax² + x + 3

Factor theorem states that , if f(x) be a polynomial then x - a is a factor of f(x) iff f(a) = 0

So by factor theorem we get

$\displaystyle \sf f( - 3) = 0$

$\displaystyle \sf{ \implies } {( - 3)}^{3} + a \times {( - 3)}^{2} + ( - 3) + 3 = 0$

$\displaystyle \sf{ \implies } - 27 + 9a - 3 + 3 = 0$

$\displaystyle \sf{ \implies } 9a = 27$

$\displaystyle \sf{ \implies } a = \frac{27}{9}$

$\displaystyle \sf{ \implies } a =3$

Hence the required value of a = 3

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