Determine whether each trinomial is a perfect square trinomial. If so factor it?

Question

n square + 6n + 3

and m square - 12m + 36

Answer 1

n² + 6n + 3 is not a perfect square. I can be solved by completing the suare or the Quadratic formule.

m² - 12m + 36 can be factored

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m² - 12m + 16

m² - 6m - 6m + 36

m(m - 6) - 6(m - 6)

(m - 6)(m - 6)

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Answer 2

Trinomial number 1) is not a perfect square., The trinomial number two is a perfect square and it can be factorized as:

(m - 6)(m - 6) = (m-6)^2

One way to determine if it's a trinomial is perfect square is using the following formula:

(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2

In the second trinomial notice that:

b^2 = 36, so b = +/- 6 (square root, remeber that when you find a square root, the solution might be neg. or positive). Also notice that 6 must be negative, since 2ab must be negative. since a = m then 2(m)(-6) = -12m

Hence the trinomal can be factorized as (m - 6)^2 with a = m, b = -6

Answer 3

Perfect square trinomials are of the form ax^2+2abx+b^2

n^2 + 6n + 3 ------ not a perfect square trinomial

m^2 - 12m + 36 = (m-6)^2

Answer 4

The first one isn't because 3 isn't a square.
The constant term of a square trinomial must be a square.
To check the second one, compute the discriminant:
b²-4ac = 144-4(36) = 0.
That means m²-12m+36 is a square and we have
m²-12m+36 = (m-6)².

Answer 5

1st isn't
2nd =(m-6)^2

Perfect square trinomials are of the form a^2x^2+2abx+b^2

Answer 6

The 1st one is not

2.) (m-6)^2