AnswersAlgebra I CR GTMultiplying Polynomials and Simplifying Expressions

Multiplying Polynomials and Simplifying Expressions Answers

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The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2. Which expression is equivalent to this product after it has been fully simplified?

A
x3 + 5x2 + 5x – 2
B
x3 + 2x2 + 8x – 2
C
x3 + 11x2 – 2
D
x3 + 10x2 – 2
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What is the product of (3a + 2)(4a2 – 2a + 9)?

A
12a3 − 2a + 18
B
12a3 + 6a + 9
C
12a3 − 6a2 + 23a + 18
D
12a3 + 2a2 + 23a + 18
3

Chin made an error in his chart showing the multiplication of the binomial by the trinomial.

Question illustration
A
The expression 3x3 should be 3x2.
B
The expression 6x should be 6xy.
C
The expression x2y should be x2y2.
D
The expression 4y should be 4y2.
4

What is the product of a+3 and −2a2+15a+6b2?

A
−2a3+9a2+45a+24b2
B
−2a3+21a2+45a+24b2
C
−2a3+9a2+45a+6ab2+18b2
D
−2a3+21a2+45a+6ab2+18b2
5

Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.(2x)(x2) + (2x)(x) + (2x)(–2) + (3)(x2) + (3)(x) + (3)(–2)Which is the simplified product?

A
2x3 + 6x2 – x – 6
B
2x3 + x2 – x – 6
C
2x3 + 5x2 – x – 6
D
2x3 – x2 – 7x – 6
6

The polynomial x3 + 8 is equal to

A
(x + 2)(x2 – 2x + 4).
B
(x – 2)(x2 + 2x + 4).
C
(x + 2)(x2 – 2x + 8).
D
(x – 2)(x2 + 2x + 8).
7

Fiona wrote out the description of each step for her multiplication of the binomial and trinomial (2x – 3)(5x2 – 2x + 7).In which step did Fiona make an error?

Question illustration
A
Step 1
B
Step 2
C
Step 3
D
Step 4
8

Use the chart to multiply the binomial by the trinomial.

Question illustration
A
y3 + 27
B
y3 – 27
C
y3 – 6y2 + 27
D
y3 + 6y2 + 27
9

The variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x – 3. What is AB – C2 in simplest form?

A
3x3 + 2x2 – x + 3
B
3x3 + 2x2 – x – 3
C
3x3 + x2 – 6x + 9
D
3x3 + x2 + 6x – 9
10

Iliana multiplied 3p – 7 and 2p2 – 3p – 4. Her work is shown in the table.

Question illustration
A
6p3 + 23p2 + 9p + 28
B
6p3 – 23p2 – 9p + 28
C
6p3 – 23p2 + 9p + 28
D
6p3 + 23p2 – 9p + 28

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