Factoring Trinomials: a > 1 — Quiz

Question 3 • Algebra I

Which model represents the factors of 4 x squared negative 9 ?

Answer

Image with description An algebra tile layout with tiles arranged in a grid. Along the top row are 2 tiles labeled positive x, followed by 3 tiles each labeled negative 1. Along the left side are 2 tiles each labeled positive x, followed by 3 tiles each labeled positive 1. Inside the main grid, the upper left section contains 4 large square tiles each labeled positive x squared, arranged in 2 rows and 2 columns. To the right of the upper positive x squared tiles in the first row are 3 rectangular tiles each labeled positive x. To the right of the lower positive x squared tiles in the second row are 3 rectangular tiles each labeled negative x. Below the positive x squared tiles are 3 rectangular tiles each labeled positive x, arranged in 3 rows and 1 column. To the right of these are 3 rectangular tiles each labeled negative x, arranged in 3 rows and 1 column. In the lower right section are 9 small square tiles each labeled negative 1, arranged in 3 rows and 3 columns.

Image with description An algebra tile layout with tiles arranged in a grid. Along the top row are 2 tiles labeled positive x, followed by 3 tiles each labeled positive 1. Along the left side are 2 tiles each labeled positive x, followed by 3 tiles each labeled positive 1. Inside the main grid, the upper left section contains 4 large square tiles each labeled positive x squared, arranged in 2 rows and 2 columns. To the right of the upper positive x squared tiles in the first row are 3 rectangular tiles each labeled positive x. To the right of the lower positive x squared tiles in the second row are 3 rectangular tiles each labeled negative x. Below the positive x squared tiles in the first column are 3 rectangular tiles each labeled positive x, arranged in 3 rows and 1 column. To the right of these are 3 rectangular tiles each labeled negative x, arranged in 3 rows and 1 column. In the lower right section are 9 small square tiles each labeled positive 1, arranged in 3 rows and 3 columns.

Image with description An algebra tile layout with tiles arranged in a grid. Along the top row are 2 tiles labeled positive x, followed by 3 tiles each labeled positive 1. Along the left side are 2 tiles each labeled positive x, followed by 3 tiles each labeled negative 1. Inside the main grid, the upper left section contains 4 large square tiles each labeled positive x squared, arranged in 2 rows and 2 columns. To the right of the positive x squared tiles are 6 rectangular tiles each labeled positive x, arranged in 2 rows and 3 columns. Below the positive x squared tiles are 6 rectangular tiles each labeled negative x, arranged in 3 rows and 2 columns. In the lower right section are 9 small square tiles each labeled negative 1, arranged in 3 rows and 3 columns.

Image with description An algebra tile layout with tiles arranged in a grid. Along the top row are 2 tiles labeled positive x, followed by 3 tiles each labeled negative 1. Along the left side are 2 tiles each labeled positive x, followed by 3 tiles each labeled negative 1. Inside the main grid, the upper left section contains 4 large square tiles each labeled positive x squared, arranged in 2 rows and 2 columns. To the right of the positive x squared tiles are 6 rectangular tiles each labeled negative x, arranged in 2 rows and 3 columns. Below the positive x squared tiles are 6 rectangular tiles each labeled negative x, arranged in 3 rows and 2 columns. In the lower right section are 9 small square tiles each labeled negative 1, arranged in 3 rows and 3 columns.

Explanation

The expression 4x² − 9 is a difference of squares: (2x)² − 3² = (2x + 3)(2x − 3). The model should therefore have positive x tiles along both dimensions, positive 1 tiles on one side and negative 1 tiles on the other, producing +6x and −6x cross terms and nine −1 tiles. Choice C shows those signs and tiles, so it represents the factors.

AI-written and checked against the verified answer.

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