Question

Find the value of a if x+6 is a factor of x3+3x2+4x+a

Answer 1

Heya friend,

Here is the answer:

x+6=0

x= -6

p(x)=x^3+3x^2+4x+k

p(-6)= (-6)^3+3(-6)^2+4(-6)+k=0

Therefore,

= -216+108-24+k=0

= -240+108+k=0

= -132+k=0

=k= +132

Hope my answer helps you :)

Regard

Succerjb

Answer 2

Given:

Expression: x³+3x²+4x+a

The factor of the expression= x+6

To find:

The value of a

Solution:

The value of a is 132.

We can find the value by following the given steps-

We know that the factor completely divides a number and leaves no remainder.

Similarly, on dividing the expression by x+6, the value of the equation becomes 0.

So, we can equate the factor with 0 to get the value of the variable which is also the root of the given expression.

On putting x+6=0, we get

x= -6

Now, if we put x= -6 in x³+3x²+4x+a, its value becomes 0.

Putting x= -6 in the expression,

(-6)³+3(-6)²+4(-6)+a=0

-216+108-24+a=0

-132+a=0

a=132

Therefore, the value of a is 132.