Question 1

Given the image above, which represents a square potholder, Rebekah wants to make a potholder with an area of $9x^2 - 6x + 1$ square inches. What is the expression for the side length of the potholder?

Accepted Answer

$3x - 1$

Question 2

Which of the following is a perfect square trinomial?

Accepted Answer

$x^2 + 10x + 25$

Question 3

Factor the trinomial $x^2 - 6x + 9$.

Accepted Answer

$(x - 3)^2$

Question 4

Which of the following steps is NOT part of the checklist for identifying a perfect square trinomial?

Accepted Answer

Check if the polynomial is a difference of squares.

Question 5

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

Accepted Answer

$2x^2 - 26x + 144$

Question 6

Factor the trinomial $9x^2 + 12x + 4$.

Accepted Answer

$(3x + 2)^2$

Question 7

Which of the following is the correct factorization for $25x^2 - 60x + 36$?

Accepted Answer

$(5x - 6)^2$

Question 8

Mrs. Carter writes $x^2 + bx + 64$ on the board as a perfect square trinomial, but the middle term is erased. Declan claims $b = 16$. Is there another possibility?

Accepted Answer

Yes, $b$ could also be $-16$.

Question 9

Which of the following is a real-world application of perfect square trinomials?

Accepted Answer

Calculating the area of a square garden with a side length expressed as a binomial.

Question 10

Write a perfect square trinomial that includes the term $36x^2$.

Accepted Answer

$36x^2 + 60x + 25$

Question 11

Which of the following is the correct factorization for $16h^2 - 72h + 81$?

Accepted Answer

$(4h - 9)^2$

Question 12

Which of the following is the correct factorization for $36r^2 - 48r + 16$?

Accepted Answer

$(6r - 4)^2$

Question 13

Which of the following is NOT a perfect square trinomial?

Accepted Answer

$25x^2 + 15x - 4$

Question 14

Which of the following is the correct factorization for $4x^2 + 28x + 49$?

Accepted Answer

$(2x + 7)^2$

Question 15

Which of the following is the correct factorization for $x^2 + 26x + 169$?

Accepted Answer

$(x + 13)^2$

Factoring Perfect Square Trinomials – College Algebra Study Guide

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