Question

which are perfect square trinomials? select two options A. x^2 -9 B. x^2 -100 C. x^2 - 4x + 4 D. x^2 +10x +25 E. x^2 +15x + 36​

Answer 1

C and D
x^2 - 4x + 4 = (x-2)^2
x^2 + 10x +25 = (x+5)^2

Answer 2

C.
`x^2 - 4x + 4`

D.
`x^2 +10x +25`

Explanation:

A trinomial
`ax^2+bx+c` is perfect square trinomial if,

`D=b^2 - 4ac = 0`,

A.
`x^2 -9`

By comparing,

a = 1, b = 0, c = -9,

`0^2 - 4* 1* -9\\eq 0`

⇒ it is not a perfect square trinomial.

B.
`x^2 -100`

By comparing,

a = 1, b = 0, c = -100,

`0^2 - 4* 1* -100\\eq 0`

⇒ it is not a perfect square trinomial.

C.
`x^2 - 4x + 4`

By comparing,

a = 1, b = -4, c = 4,

`(-4)^2 - 4* 1* 4=16-16=0`

⇒ it is a perfect square trinomial.

D.
`x^2 +10x +25`

By comparing,

a = 1, b = 10, c = 25,

`10^2 - 4* 1* 25=100-100=0`

⇒ it is a perfect square trinomial.

E.
`x^2 +15x + 36`

By comparing,

a = 1, b = 15, c = 36,

`15^2 - 4* 1* 36=225-144=81\\eq 0`

⇒ it is not a perfect square trinomial.