AnswersCommon Core Algebra I B-ICFactoring Polynomials Completely

Factoring Polynomials Completely — Unit test Answers

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Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 – 40x + 25 square inches.

Question illustration
A
4x + 5
B
4x – 5
C
8x + 5
D
8x – 5
2
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A square with an area of A2 is enlarged to a square with an area of 25A2. How was the side of the smaller square changed?

A
The side length was increased by 5.
B
The side length was multiplied by 5.
C
The side length was increased by 10.
D
The side length was multiplied by 10.
3

What is the greatest common factor of the terms in the polynomial 12x4 + 27x3 + 6x2?

A
3x
B
3x2
C
6x2
D
6x4
4

Which binomial is a factor of 9x2 – 64?

A
3x – 8
B
9x – 32
C
3x + 32
D
9x + 8
5

What is the greatest common factor of the terms in the polynomial 8x4 – 4x3 – 18x2?

A
2x
B
2x2
C
4x
D
4x2
6

The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24?

A
y – 20
B
y – 14
C
y – 8
D
y – 6
7

Tyrone factored the polynomial completely. What is the value of B?12x4+30x3+4x2+10xAx(Bx2+1)(2x+5)

A
2
B
3
C
5
D
6
8

Which monomials are perfect squares? Select three options.

A
6x2
B
9x8
C
17x9
D
25x12
E
36x16
9

Which is the completely factored form of 12x3 – 60x2 + 4x – 20?

A
4(3x2 – 1)(x – 5)
B
4x(3x2 + 1)(x – 5)
C
4x(3x2 – 1)(x + 5)
D
4(3x2 + 1)(x – 5)
10

How could Brent use a rectangle to model the factors of x2 – 7x + 6?

A
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
B
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
C
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
D
He could draw a diagram of a rectangle with dimensions x – 4 and x + 3 and then show the area is equivalent to the sum of x2, –4x, 3x, and half of –12.
11

The diagram represents a difference of squares.

Question illustration
A
(m – 2)(m + 18)
B
(m – 3)(m + 3)
C
(m – 4)(m + 9)
D
(m – 6)(m + 6)

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