Factoring Polynomials: GCF Answers

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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).
2
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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.
3

What is the product?(4y − 3)(2y2 + 3y − 5)

A
8y3 + 3y + 15
B
8y3 − 23y + 15
C
8y3 − 6y2 − 17y + 15
D
8y3 + 6y2 − 29y + 15
4

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
5

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
6

What is the product?(x − 3)(2x2 − 5x + 1)

A
2x3 − x2 + 16x + 3
B
2x3 − 11x2 + 16x + 3
C
2x3 − 11x2 + 16x − 3
D
2x3 − x2 + 16x − 3
7

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
8

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
9

Use the chart to multiply the binomial by the trinomial.

Question illustration
A
15y3 + 17y2 + 22y + 15
B
6y3 + 17y2 + 22y + 15
C
6y3 + 20y2 + 22y + 15
D
6y3 + 17y2 + 22y + 25
10

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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Factoring Polynomials: GCF Answers — Summer 2026…