Answer:
Option (c) is correct.
The expression becomes [tex]x^2+6x+9=(x+3)^2[/tex]
Step-by-step explanation:
Given expression [tex]x^2+6x[/tex]
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 [tex]x^2+6x[/tex]
To make it a perfect square trinomial convert the given expression in the form of perfect square
Using the identity [tex](a+b)^2=a^2+2ab+b^2[/tex]
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 [tex]b^2[/tex] term ,
That is [tex]b^2=9[/tex]
Thus, the expression becomes [tex]x^2+6x+9=(x+3)^2[/tex]
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
