Question 1

Which of the following is the correct factorization of the perfect square trinomial $$4x^2 - 28x + 49$?

Accepted Answer

$$ (2x - 7)^2$ $$

Question 2

Given the trinomial $$4x^2 - 28x + 49$, which step is necessary to confirm it is a perfect square trinomial?

Accepted Answer

Check if the first and last terms are perfect squares and if the middle term is twice the product of their square roots.

Question 3

If $$4x^2 - 28x + 49$ models the area of a square garden in square meters, what is the length of one side of the garden in terms of x$?

Accepted Answer

$$2x - 7$$

Question 4

Which of the following trinomials is also a perfect square trinomial?

Accepted Answer

$$9x^2 - 24x + 16$

Question 5

What is the expanded form of $$(2x - 7)^2$?

Accepted Answer

$$4x^2 - 28x + 49$

Question 6

A rectangular plot has an area given by $$4x^2 - 28x + 49$ square feet. If the plot is actually a square, what is the perimeter in terms of x$?

Accepted Answer

$$8x - 28$$

Question 7

Which of the following is NOT a characteristic of a perfect square trinomial?

Accepted Answer

The trinomial must have all positive terms.

Question 8

If $$4x^2 - 28x + 49$ represents the cost (in dollars) to produce x$ items, what is the minimum cost and for what value of x$ does it occur?

Accepted Answer

The minimum cost is $$0 at$$ $$x = \frac{7}{2}$$

Question 9

Which of the following expressions is equivalent to $$4x^2 - 28x + 49$?

Accepted Answer

$$(2x - 7)(2x - 7)$$

Question 10

If $$4x^2 - 28x + 49$ is the area of a square, and you want to double the side length, what will be the new area in terms of x$?

Accepted Answer

$$16x^2 - 112x + 196$

Factoring a Perfect Square Trinomial

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