Question

A perfect square trinomial can be represented by a square model with equivalent length and width. Which polynomial can be represented by a perfect square model?
a. x2 – 6x + 9
b. x2 – 2x + 4
c. x2 + 5x + 10
d. x2 + 4x + 16

Answer 1

The correct answer is 
$A) x^2 - 6x + 9$

In fact, this is a trinomial of the form $ax^2-bx+c$, whose solutions are given by
$x_{1,2}= \frac{-b\pm \sqrt{b^2 -4ac} }{2a}$
Using this formula for the trinomial of the problem, we find:
$x1,2= \frac{6 \pm \sqrt{6^2-4\cdot 1\cdot 9}}{2} =3$
we see that this trinomial has two coincident solutions (x=3 with multiplicity 2). This means that it can be rewritten as a perfect square, in the following form: 
$(x-3)^2$

Answer 2

Answer:

a. x2 – 6x + 9

Step-by-step explanation:

In order to solve this you just have to try and factorize the options and the result should be two exact binomials. Remember that the formula for perfect square trinomial is:

$a^{2} +2ab+b^{2} =(a+b)(a+b)$

So we only have to factorize x2-6x+9=

As you can see, a is equal to X, and b equals 3:

(x-3)(x-3)=x2-6x+9

SO this is a perfect square trinomial.