Question

3x^3+ax+3x+5is divided by x-2 find the value of a

Answer 1

Answer:

$\large a=-\dfrac{35}{2}$

Step-by-step explanation:

Given :

$\large p(x)=3x^3+ax+3x+5 \ and \ g(x)=x-2$

And p ( x ) is divisible by ( x - 2 ) mean ( x - 2 ) is a factor of p ( x ) .

Zeroes of g ( x )

x - 2 = 0

x = 2

Now putting x = 2 in p ( x ) we get values of a

$\large p(x)=3x^3+ax+3x+5\\\\\\\large p(2)=3(2)^3+2a+3(2)+5=0\\\\\\\large p(2)=3\times8+2a+6+5=0\\\\\\\large p(2)=24+2a+11=0\\\\\\\large 35+2a=0\\\\\\\large 2a=-35\\\\\\\large a=-\dfrac{35}{2}$

Thus we get value of  $\large a=-\dfrac{35}{2}$

Answer 2

Answer: $\tt {a = \frac {(-35)}{2}}$

Step-by-Step explanation:

$\tt {p (x) = 3x^{3} + ax+ 3x + 5}$ is divisible by (x - 2), this means, (x - 2) is a factor of p (x).

If (x - 2) is a factor of p (x), then, we should get the remainder as equal to 0 when we divide them.

First, we will find the value of x:

x - 2 = 0

=> x = 2

Now, we will put the value of x in p (x) and solve it as shown:

=> $\tt {p (x) = 3x^{3} + ax+ 3x + 5}$

Solve this equation further:

=> $\tt {p (2) = 3((2)^{3}) + a(2)+ 3(2) + 5}$

This will be equal to 0 as shown below:

=> $\tt {p (2) = 24 + 2a+ 6 + 5 = 0}$

=> p (2) = 35 + 2a = 0

=> $\tt {a = \frac {(-35)}{2}}$