create a perfect square trinomial that can be factored using special patterns. Factor the trinomial and show all work for full credit.

trinomial is 3 terms
ax^2+bx+c
4 is a perfect square since 2*2
essentially, you need (x+a)^2
(x+1)^2=(x+1)(x+1)=x^2+2x+1
as far as "special patterns" this may imply that you need to find a perfect square trinomial that requires a different factoring process, I'm not sure what that means

Answer Link

JeanaShupp JeanaShupp · Answer 2 · 2018-12-12T08:59:41+01:00

Answer: [tex]4x^2+12x+9[/tex]

Step-by-step explanation:

A perfect square trinomial is written as [tex]ax^2+bx+c[/tex], where

first term [tex]ax^2[/tex] = square of first term of binomial

second term=[tex]bx[/tex]=twice the product of both terms of binomial.

and third term 'c'=square of last term of binomial

Thus to create a perfect square trinomial put 'a' and 'c' a square number

Let a=4 and c=9

The required trinomial will be

[tex]4x^2+12x+9[/tex]

[tex]=(2x)^2+2(2x)(3)+3^2\\=(2x+3)^2.......\text{[using pattern}(a+b)^2=a^2+2ab+b^2]\\=(2x+3)(2x+3)[/tex]