Polynomial Expressions — Test

Question 21 • Algebra 1

Which model represents the factors of x squared plus 9 x plus 8 ?

Answer

Image with description An algebra tile configuration. 6 tiles are in the Factor 1 spot: 1 is labeled + x and 5 are labeled +. 4 tiles are in the Factor 2 spot: 1 is labeled + x and 3 are labeled +. 24 tiles are in the Product spot: 1 is labeled + x squared, 8 are labeled + x, 9 are labeled +, and 6 are labeled negative.

Image with description An algebra tile multiplication grid illustrates a polynomial multiplication layout with factors along the top and left headers. The horizontal top header consists of nine tiles representing the expression x plus eight, organized as one rectangle labeled plus x and eight small squares labeled with a plus sign. The vertical left header consists of two tiles representing the expression x plus one, organized as one rectangle labeled plus x and one small square labeled with a plus sign. Inside the main product grid, the top row contains one large square tile labeled plus x squared followed by eight vertical rectangle tiles labeled plus x. Below this row, the remaining filled space features one horizontal row containing one horizontal rectangle tile labeled plus x followed by eight small square tiles labeled with a plus sign.

Image with description An algebra tile multiplication grid illustrates a polynomial multiplication layout with factors along the top and left headers. The horizontal top header consists of seven tiles representing the expression x plus six, organized as one rectangle labeled plus x and six small squares labeled with a plus sign. The vertical left header consists of four tiles representing the expression x plus three, organized as one rectangle labeled plus x and three small squares labeled with a plus sign. Inside the main product grid, the top row contains one large square tile labeled plus x squared followed by six vertical rectangle tiles labeled plus x. Below this row, the left side features three horizontal rectangle tiles labeled plus x and a three-by-three grid of small square tiles labeled with a plus sign. The remaining bottom right section of the grid is filled out by a three-by-three grid of small square tiles labeled with a minus sign.

Image with description An algebra tile multiplication grid illustrates a polynomial multiplication layout with factors along the top and left headers. The horizontal top header consists of five tiles representing the expression x plus four, organized as one rectangle labeled plus x and four small squares labeled with a plus sign. The vertical left header consists of three tiles representing the expression x plus two, organized as one rectangle labeled plus x and two small squares labeled with a plus sign. Inside the main product grid, the top row contains one large square tile labeled plus x squared followed by four vertical rectangle tiles labeled plus x. Below this row, the remaining space is filled out by two horizontal rows, each featuring one horizontal rectangle tile labeled plus x followed by four small square tiles labeled with a plus sign, completing a two-by-four grid of small square tiles in the bottom right corner.

Explanation

Factor x² + 9x + 8 by finding two numbers that multiply to 8 and add to 9: 1 and 8. Thus, x² + 9x + 8 = (x + 1)(x + 8). Choice B shows those factors, and its product grid contains x², eight x-tiles, one more x-tile, and eight unit tiles, for a total of x² + 9x + 8.

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