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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

User Ryan Walls
by
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2 Answers

5 votes

Answer:

a. x2 – 6x + 9

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.

User Ankit Chandora
by
7.9k points
4 votes
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)= (-b\pm √(b^2 -4ac) )/(2a)
Using this formula for the trinomial of the problem, we find:

x1,2= (6 \pm √(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
User Psychologeek
by
7.4k points

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