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

Answer:

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

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

Step-by-step 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,

$0^2 - 4\times 1\times -9\neq 0$

⇒ it is not a perfect square trinomial.

B. $x^2 -100$

By comparing,

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

$0^2 - 4\times 1\times -100\neq 0$

⇒ it is not a perfect square trinomial.

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

By comparing,

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

$(-4)^2 - 4\times 1\times 4=16-16=0$

⇒ it is a perfect square trinomial.

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

By comparing,

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

$10^2 - 4\times 1\times 25=100-100=0$

⇒ it is a perfect square trinomial.

E.  $x^2 +15x + 36$

By comparing,

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

$15^2 - 4\times 1\times 36=225-144=81\neq 0$

⇒ it is not a perfect square trinomial.