Verified Answer :

Answer:

Option (c) is correct.

The expression becomes \(x^2+6x+9=(x+3)^2\)

Step-by-step explanation:

Given expression \(x^2+6x\)

We have to find the number that must be added to the given expression so that it change it into a perfect square trinomial.

Consider the given expression \(x^2+6x\)

To make it a perfect square trinomial convert the given expression in the form of perfect square

Using the identity \((a+b)^2=a^2+2ab+b^2\)

Compare the given expression we have

a = x   ....(1)

⇒ 2ab = 6x  

From (1) , we have

⇒ 2b = 6

⇒ b = 3

Thus, to make perfect square we have to add \(b^2\) term ,

That is  \(b^2=9\)

Thus, the expression becomes  \(x^2+6x+9=(x+3)^2\)

Option (c) is correct.

The number 9 should be added to the expression x² + 6x to change it into a perfect square trinomial that will become (x + 3)².

What is the perfect square polynomial?

A perfect square trinomial is an algebraic expression that is of the form ax²+bx+c, which has three-term. It is obtained by the multiplication of binomial with itself.

Given

x² + 6x + c is a polynomial.

To find

The value of c.

We know the formula

(a + b)² = a² + 2ab + b²

Similarly

(x + a)² = x² + 2ax + a²= x² + 6x + a²

Compare the eqaution

2ax = 6x a = 3

then

c = a² = 3² = 9

Then the value of c is 9.

Thus number 9 should be added to the expression x²+6x to change it into a perfect square trinomial.

More about the perfect square polynomial link is given below.

https://brainly.com/question/88561