AnswersAlgebra 1Polynomial Expressions

Polynomial Expressions — Test Answers

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21
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Which model represents the factors of x squared plus 9 x plus 8 ?

A
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.
B
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.
C
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.
D
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.
22
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Which algebraic expression is a polynomial with a degree of 4 ?

A
2 x to the 4th power minus 6 x to the 4th power plus 14 over x
B
x to the 5th power minus 6 x to the 4th power plus 14 x cubed plus x squared
C
9 x to the 4th power minus x cubed minus x over 5
D
5 x to the 4th power plus square root of 4 x
23

Manuel did not write the remainder. What is the remainder over the divisor?

A
negative the fraction with numerator 18 and denominator A plus 3
B
negative the fraction with numerator 18 and denominator A squared minus 4 A plus 3
C
the fraction with numerator 24 and denominator A plus 3
D
the fraction with numerator 24 and denominator A squared minus 4 A plus 3
24

Which product should Tomas choose?

A
open paren 2 x plus y close paren times open paren 2 x squared minus 2 x y plus y squared close paren
B
open paren 2 x plus y close paren times open paren 2 x squared plus 2 x y minus y squared close paren
C
open paren 2 x plus y close paren times open paren 4 x squared minus 2 x y plus y squared close paren
D
open paren 2 x plus y close paren times open paren 4 x squared plus 2 x y minus y squared close paren
25

Which simplified expression represents the area of the parallelogram?

A
2 x cubed minus 6 x squared minus 14 x plus 24 square centimeters
B
2 x cubed plus 6 x squared plus 14 x plus 24 square centimeters
C
negative 4 x cubed plus 14 x minus 24 square centimeters
D
negative 4 x cubed minus 14 x plus 24 square centimeters

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Polynomial Expressions — Test Answers — Algebra 1