Respuesta :
The polynomial a,b,c,are not perfect square polynomial and the polynomial d is perfect square polynomial.
The given polynomial is
[tex]a) 36x^2-4x+16[/tex]
What is the form of perfect square polynomial?
[tex](ax+b)^2[/tex]
we solve this method by using perfect square method
add and subtract 1/9
[tex]36x^2-4x+16+\frac{1}{9}-\frac{1}{9}[/tex]
factor 36
[tex]\frac{143}{9}+36(x^2-\frac{x}{9}+\frac{1}{324} )[/tex]
Now complete the square
[tex]\frac{143}{9}+36(x^2-\frac{1}{18})^2[/tex]
Therefore this is not perfect square trinomial.
Similarly for
[tex]b) 16x^2-8x+36[/tex]
Complete square is,
[tex]16(x-\frac{1}{4})^2+35[/tex]
This polynomial is also not perfect square trinomial.
[tex]c) 25x^2+9x+4\\[/tex]
complete square is,
[tex]25(x+\frac{9}{50})^2+\frac{319}{100}[/tex]
This polynomial is not perfect square trinomial.
[tex]d)4x^2+20x+25\\[/tex]
complete square is,
[tex](2x+5)^2[/tex]
This polynomial is perfect square trinomial.
Therefore,
The polynomial a,b,c,are not perfect square polynomial and the polynomial d is perfect square polynomial.
To learn more about perfect square trinomial visit:
https://brainly.com/question/1538726
