Answer:
4x^2 - 12x + 9
Step-by-step explanation:
Please use " ^ " to denote exponentiation: 4x^2 - 12x + 9.
This 4x^2 - 12x + 9 factors into (2x - 3)^2, and is thus a perfect square trinomial.
The polynomial [tex]4x^2-12x + 9[/tex] is a perfect square trinomial. It has a binomial factor (2x - 3).
The product of a binomial by itself gives the perfect square trinomial.
A trinomial is a polynomial that has only three terms and A binomial is a polynomial that has only two terms.
A. Trinomial [tex]4x^2-12x+9[/tex]
⇒ [tex](2x)^2-2(2x)(3)+(3)^2[/tex]
This is in the form of [tex]a^2-2ab+b^2[/tex] . So, we can write [tex](a - b)^2[/tex]
⇒ [tex](2x - 3)^2[/tex] or (2x - 3)(2x - 3)
Thus, this is a perfect square trinomial.
B. Trinomial [tex]16x^2+24x-9[/tex]
⇒ [tex](4x)^2+2(4x)(3)-(3)^2[/tex]
Since it cannot split into a binomial square, this trinomial is not a perfect square trinomial.
C. Trinomial [tex]4a^2-10a+25[/tex]
⇒ (2a)^2-2(5a)+(5)^2
This cannot be split into a binomial square, this is not a perfect square trinomial.
D. Trinomial [tex]36b^2-24b-16[/tex]
⇒ [tex](6b)^2-2(6b)(2)-(4)^2[/tex]
So, this is not a perfect square trinomial.
Therefore, the trinomial at option A is a perfect square trinomial.
Learn more about the perfect square trinomial here:
https://brainly.com/question/2751022
#SPJ2
