Question 31

Question

Factor completely
25m² - 9
*
1 point
A. (5n + 3)(5n - 3)
B. (4n - 1)²
C. (5n - 3)²
D. (25n + 9)²
Question 32
Factor Completely
n² + n - 72
*
1 point
A. (n+36)(n-2)
B. (n+9)(n-8)
C. (n-9)(n+8)
D. (n+12)(n-6)
E. (n-12)(n+6)
Question 33
Jacob incorrectly factored 5x² - 11x + 2 using the following steps:
Step 1: 5x² + (-10x - x) + 2
Step 2: (5x² - 10x)+(x - 2)
Step 3: 5x (x - 2) + 1(x - 2)
Step 4: (5x + 1)(x - 2)
In which step did he make his first error?
*
1 point
A. In Step 1 because the -11x was rewritten as -10x - x.
B. In Step 2 because the sign on x should be negative and the sign on 2 should be positive.
C. In Step 3 because there is no need to multiply (x - 2 ) by 1.
D. In Step 4 because (x - 2) should be written first.

Answer 1

Here are the answers for each question:

Question 31
Factor completely: \( 25m^2 - 9 \)

This is a difference of squares, which can be factored as follows: \[ 25m^2 - 9 = (5m)^2 - (3)^2 = (5m + 3)(5m - 3) \]

Correct answer: A. (5m + 3)(5m - 3)

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Question 32
Factor completely: \( n^2 + n - 72 \)

To factor, we need two numbers that multiply to -72 and add to 1. These numbers are 9 and -8. So we have: \[ n^2 + n - 72 = (n + 9)(n - 8) \]

Correct answer: B. (n + 9)(n - 8)

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Question 33
In which step did Jacob make his first error?

Let's examine the steps:

• Step 1: He rewrote \(-11x\) as \(-10x - x\), which is incorrect because it should stay as \(-11x\).
• Step 2: He grouped terms but is following from an incorrect Step 1.
• Step 3: He factored out \(5x\) and \(1\) correctly based on what he had, but it stemmed from the error in Step 1.
• Step 4: Factoring is not affected by the order, so it's not an error.

The first error occurred in Step 1.

Correct answer: A. In Step 1 because the -11x was rewritten as -10x - x.