Question

If x+1 is a factor of the polynomial 3x^2-kx.find the value of k

Answer 1

Given,

x+1 is a factor of the polynomial (3x²-kx)

To find,

The value of k

Solution,

Since x + 1 is a factor of  3x²-kx , hence x = -1 is a solution of equation of given equation.

⇒ 3x²-kx=0

⇒ Put x = -1

⇒ 3(-1)² -k(-1) = 0

⇒ 3 + k = 0

⇒ k = -3.

Hence, the value of k so that x+1 is a factor of the polynomial 3x²-kx is -3.

We can also verify our solution,

3x²-kx=0

Now, put k = -3.

⇒  3x²-(-3)x=0

⇒  3x²+3x=0

⇒  Put x = -1

⇒  3(-1)²+3(-1)=0

⇒  3 - 3 = 0.

Answer 2

given a polynomial $3x^2-kx$ and its factor $x+1$, find k

Explanation:

1. as we know that for a given a polynomial $x^2+(a+b)x+ab$ (where a and b are real numbers) can be factorized and be evaluated as , $x^2+(a+b)x+ab= (x+a)(x+b)$    
2. hence given a polynomial $3x^2-kx$                                                                                            

                                                 =>$3x(x-\frac{k}{3} )$                              

    3. hence, $3x\ and\ x-\frac{k}{3}$ are factors of the given polynomial.

    4. given $x+1$ is a factor of polynomial we can say that,            

                                                     $x+1=x-\frac{k}{3} \\\frac{k}{3}=-1\\k=-3$          

    5. hence the value of k such that $3x^2-kx$ has a factor $x+1$ is $-3$