The factor of the trinomial is [tex](2x+3)^2[/tex]
Explanation:
The given trinomial is [tex]4x^{2} +12x+9[/tex]
We need to determine the factor of the trinomial.
The factor of the trinomial can be determined by finding the root of the trinomial.
Let us factorize the trinomial [tex]4x^{2} +12x+9[/tex]
Thus, the trinomial can be written as,
[tex]4x^{2} +6x+6x+9[/tex]
Grouping the terms, we have,
[tex]2x(2x +3)+3(2x+3)[/tex]
Simplifying the terms, we get,
[tex](2x+3)(2x+3)[/tex]
Multiplying the terms, we have,
[tex](2x+3)^2[/tex]
Thus, the factor of the trinomial is [tex](2x+3)^2[/tex]
