AnswersFall 24 GMS Algebra Concepts and Connections AAdding and Subtracting Rational Expressions (Continued)

Introduction to Polynomials Answers

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An algebra tile configuration. There are 3 large tiles, 5 tiles each half the size of a large tile, and 8 tiles each one-quarter the size of a large tile. Two of the large tiles are labeled plus x squared and 1 is labeled negative x square. Two smaller tiles are labeled plus x and 3 are labeled negative x. Six of the smallest tiles are labeled + and 2 are labeled minus.

Question illustration
A
x2 – x – 4
B
x2 – x + 4
C
3x2 – 5x + 8
D
3x2 – 5x – 8
2
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Which is true about the polynomial –8m3 + 11m?

A
It is a binomial with a degree of 2.
B
It is a binomial with a degree of 3.
C
It is a trinomial with a degree of 2.
D
It is a trinomial with a degree of 3.
3

An algebra tile configuration where the 2 largest tiles are labeled plus x squared, there are 4 tiles labeled negative x, where each tile is half the size of the largest tiles, and 6 tiles labeled minus that are each one-quarter the size of the largest tile.

Question illustration
A
2x2 – 4x – 6
B
2x2 + 4x + 6
C
–2x2 – 4x – 6
D
–2x2 + 4x + 6
4

Which algebraic expression is a polynomial?

A
3m2n – +
Option A
B
– + 4m5
Option B
C
– 3mn5 +
Option C
D
7mn + +
Option D
5

Which algebraic expression is a trinomial?

A
x3 + x2 –
Option A
B
2x3 – x2
C
4x3 + x2 –
Option C
D
x6 – x +
Option D
6

Which term could be put in the blank to create a fully simplified polynomial written in standard form?8x3y2−_____+3xy2−4y3

A
x2y2
B
x3y3
C
7xy2
D
7x0y3
7

For the polynomial 6xy2−5x2y?+9x2 to be a trinomial with a degree of 3 after it has been fully simplified, what is the missing exponent of the y in the second term?

A
0
B
1
C
2
D
3
8

Which polynomial correctly combines the like terms and expresses the given polynomial in standard form?9xy3 – 4y4 – 10x2y2 + x3y + 3x4 + 2x2y2 – 9y4

A
–13y4 + 3x4 – 8x2y2 + x3y + 9xy3
B
–13y4 + x3y – 8x2y2 + 9xy3 + 3x4
C
3x4 – 8x2y2 + x3y + 9xy3 – 13y4
D
3x4 + x3y – 8x2y2 + 9xy3 – 13y4
9

Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Select five options. + 8r2s4 – 3r3s3

Question illustration
A
StartFraction 5 s Superscript 7 Baseline Over 6 EndFraction
Option A
B
s5
C
3r4s5
D
–r4s6
E
–6rs5
F
StartFraction 4 r Over s Superscript 6 Baseline EndFraction
Option F
10

Which represents the polynomial written in standard form?8x2y2 – 3x3y + 4x4 – 7xy3

A
4x4 – 3x3y + 8x2y2 – 7xy3
B
4x4 – 7xy3 – 3x3y + 8x2y2
C
4x4 + 8x2y2 – 3x3y – 7xy3
D
–7xy3 – 3x3y + 8x2y2 + 4x4

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