Rational Expressions and Factoring

Rational Expressions and Factoring

8th Grade

18 Qs

quiz-placeholder

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Rational Expressions and Factoring

Rational Expressions and Factoring

Assessment

Quiz

Mathematics

8th Grade

Hard

Created by

Roberto Layague Jr.

Used 1+ times

FREE Resource

18 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Factor the polynomial: x^2 - 5x + 6

(x + 2)(x + 3)

(x - 2)(x - 3)

(x - 4)(x - 2)

(x - 1)(x - 6)

Answer explanation

To factor x^2 - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 fit this, so the polynomial factors to (x - 2)(x - 3). Thus, the correct answer is (x - 2)(x - 3).

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify the fraction: (2x^2 + 4x) / (2x)

x^2 + 2x

x - 2

x + 2

2x + 4

Answer explanation

To simplify (2x^2 + 4x) / (2x), factor out 2x from the numerator: 2x(x + 2). Then, cancel 2x in the numerator and denominator, resulting in x + 2. Thus, the correct answer is x + 2.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Factor the polynomial: 3x^2 + 12x

3(x^2 + 4x)

x(3x + 12)

(3x + 12)(x)

3x(x + 4)

Answer explanation

To factor 3x^2 + 12x, first factor out the greatest common factor, which is 3x. This gives us 3x(x + 4). The correct choice is 3x(x + 4).

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify the fraction: (x^2 - 9) / (x + 3)

x^2 + 3

x + 3

x - 3

x - 9

Answer explanation

To simplify (x^2 - 9) / (x + 3), factor the numerator: (x - 3)(x + 3). Cancel (x + 3) from numerator and denominator, leaving x - 3. Thus, the simplified fraction is x - 3.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Factor the polynomial: x^2 + 7x + 10

(x + 1)(x + 10)

(x - 2)(x - 5)

(x + 3)(x + 4)

(x + 2)(x + 5)

Answer explanation

To factor x^2 + 7x + 10, we look for two numbers that multiply to 10 and add to 7. The numbers 2 and 5 fit this, so the polynomial factors to (x + 2)(x + 5).

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify the fraction: (4x^2 - 16) / (2x)

(4x - 16) / (2x)

(4x^2 + 16) / (2x)

(2x^2 - 8) / (x)

2(x - 2)(x + 2) / x

Answer explanation

To simplify (4x^2 - 16) / (2x), factor the numerator: 4(x^2 - 4) = 4(x - 2)(x + 2). Thus, (4(x - 2)(x + 2)) / (2x) simplifies to 2(x - 2)(x + 2) / x, which is the correct answer.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Factor the polynomial: 2x^2 - 8x

2x(x + 4)

x(2x - 8)

2x(x - 4)

2(x^2 - 4x)

Answer explanation

To factor 2x^2 - 8x, first factor out the common term 2x. This gives 2x(x - 4). The correct choice is 2x(x - 4), as it simplifies the polynomial correctly.

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