﻿ Which of the following is/are correct in factorization?

#### Checkbox Question

Which of the following is/are correct in factorization?

1. x^2-6x-16=(x-8)(x+2)

2. ×

x^2y^2-10xy+16=(xy+2)(xy+8)

3. x^2-5xy+6y^2=(x-2)(x-3)

4. ×

x^2+13xy-30y^2=(x-10y)(x-3y)

Collected in the board: Factorization

Steven Zheng posted 2 days ago

1. x^2-6x-16

=x^2-8x+2x-16

=x(x-8)+2(x-8)

=(x-8)(x+2)

Correct

2. x^2y^2-10xy+16

=x^2y^2-8xy-2xy+16

=xy(xy-8)-2(xy-8)

=(xy-2)(xy-8)

Therefore

(xy+2)(xy+8) is not correct

3. x^2-5xy+6y^2

=x^2-3xy-2xy+6y^2

=x(x-3y)-2y(x-3y)

=(x-2)(x-3)

Correct

4. x^2+13xy-30y^2

=x^2-2xy+15xy-30y^2

=x(x-2y)+15y(x-2y)

=(x+15y)(x-2y)

Therefore

(x-10y)(x-3y) is not correct

Steven Zheng posted 2 days ago

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The text contains a series of factorization problems and their solutions, with each problem being evaluated for correctness.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
﻿ Which of the following is/are correct in factorization?

#### Checkbox Question

Which of the following is/are correct in factorization?

1. x^2-6x-16=(x-8)(x+2)

2. ×

x^2y^2-10xy+16=(xy+2)(xy+8)

3. x^2-5xy+6y^2=(x-2)(x-3)

4. ×

x^2+13xy-30y^2=(x-10y)(x-3y)

Collected in the board: Factorization

Steven Zheng posted 2 days ago

1. x^2-6x-16

=x^2-8x+2x-16

=x(x-8)+2(x-8)

=(x-8)(x+2)

Correct

2. x^2y^2-10xy+16

=x^2y^2-8xy-2xy+16

=xy(xy-8)-2(xy-8)

=(xy-2)(xy-8)

Therefore

(xy+2)(xy+8) is not correct

3. x^2-5xy+6y^2

=x^2-3xy-2xy+6y^2

=x(x-3y)-2y(x-3y)

=(x-2)(x-3)

Correct

4. x^2+13xy-30y^2

=x^2-2xy+15xy-30y^2

=x(x-2y)+15y(x-2y)

=(x+15y)(x-2y)

Therefore

(x-10y)(x-3y) is not correct

Steven Zheng posted 2 days ago

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user
The text contains a series of factorization problems and their solutions, with each problem being evaluated for correctness.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS