Question

Question 3

Which of the following are perfect square trinomials? Choose all that apply.
X² + 4x +4
X²+20+100
X² +6x+9
X²+6x-9
X²-8x-16
X ²-10x+5

Answer 1

Option 1 : x² + 4x + 4

Option 2 : x² + 20x + 100

Option 3 : x² + 6x + 9

Explanation:

Looks like you got two of them right, one wrong and one missing. The first option is also a perfect square.

Here is how it evaluates:

If a trinomial expression can be a perfect square then it can be of the form (x + a)^2 = x² + 2ax + a² . Therefore the last term must be a perfect square of a number and the second term is twice the first term x and a = 2ax

So examining the choices we get

• x² + 4x + 4 = (x + 2)² Correct
• x² + 20x + 100 = (x + 5)² Correct
• x² + 6x + 9 = (x + 3)² Correct
• x² + 6x - 9 Incorrect; square cannot be negative
• x²-8x-16 Incorrect; square cannot be negative
• x^2 - 10x + 5 Incorrect; cannot be factored as (x+a)²