Question

What number should be added to the expression x2 + 4x to change it into a perfect square trinomial?

A: 1
B: 2
C:4
D:8

Answer 1

Answer:

C. 4

Step-by-step explanation:

The given expression is

$x^{2} +4x$

A perfect square trinomial is a special type of expression that can be factored into the square of binomial expression, as follows

$(x+a)^{2}=x^{2}+2ax+a^{2}$

If you use this formula, you would find that if we add the number 4 as a constant term, we would have a perfect square trinomial

$x^{2} +4x+4$

Because, it can be factored into

$(x+2)^{2}$

If we develop this square binomial, we would find that its the same than the trinomial we found

$(x+2)^{2}=x^{2}+2(x)(2)+2^{2}=x^{2} +4x+4$

Therefore, the right answer is C.

Answer 2

The number that should be added to the expression x² + 4x to change it into a perfect square trinomial is; C: 4

Method of completing the square

We are given the expression;

x² + 4x

Now, a perfect square trinomial is one that can be factored into the square of a binomial expression as follows;

(x + a)² = x² + 2ax + a²

Our given expression can be written as;

x² + 2(2x)

This means when we compare it to the perfect square trinomial, we will get; a = 2

Thus, our complete trinomial of our question will be;

x² + 4x + 2² = x² + 4x + 4

Read more about completing the square at; https://brainly.com/question/11000832