Quiz

Algebra

Factorising

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Quiz

Factorising Score: 0/10

1. Solve for x : 12x² + 17x + 6 = 0

A. x = 3 or x = 2

B. x =

\frac{3}{4}

or x =

\frac{2}{3}

C. x = -

\frac{3}{4}

or x = -

\frac{2}{3}

D. None of the above

2. Solve for x : 5x² - 23x - 10 = 0

A. x = 5 or x = - 2

B. x = 5 or x = -

\frac{2}{5}

C. x = 5 or x = -

\frac{5}{2}

D. None of the above

3. Solve for x : 9x² + 5x - 4 = 0

A. x = 1 or x = -

\frac{4}{9}

B. x = - 1 or x =

\frac{4}{9}

C. x = - 1 or x =

\frac{9}{4}

D. None of the above

4. Solve for x : x² - 10x - 56 = 0

A. x = - 4 or x = 14

B. x = 4 or x = - 14

C. x = 2 or x = 28

D. None of the above

5. Solve for x : 2x² - 33x + 45 = 0

A. x = 15 or x =

\frac{2}{3}

B. x =

\frac{3}{2}

or x = 15

C. x = 3 or x = 5

D. None of the above

6. Solve for x : x² - 6x - 91 = 0

A. x = 9 or x = 11

B. x = - 13 or x = 7

C. x = 13 or x = - 7

D. None of the above

7. Solve for x : 6x³ - 13x² + 5x = 0

A. x = 0 or x =

\frac{1}{2}

or x =

\frac{5}{3}

B. x = 0 or x = 2 or x =

\frac{3}{5}

C. x = 0 or x = 1 or x = 5

D. None of the above

8. Solve for x : 5x² - 45 = 0

A. x = 3 or x = - 3

B. x = 5 or x = 3 or x = - 3

C. x = 0 or x = 5

D. None of the above

9. Solve for x : x² + 8 = 0

A. x = 4 or x = 2

B. x = 0 or x = 3

C. x = 3 or x = 2

D. None of the above

10. Solve for x : $\frac{1}{2}$ x² + $\frac{7}{6}$ x - 1 = 0

A. x = 0 or x =

\frac{1}{2}

B. x =

\frac{2}{3}

or x = - 3

C. x = 2 or x = - 3

D. None of the above

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Quiz Results

Your score is 0 out of 10

Solutions

Factorising Question 1 of 10

1. Solve for x : 12x² + 17x + 6 = 0

A. x = 3 or x = 2

B. x =

\frac{3}{4}

or x =

\frac{2}{3}

C. x = -

\frac{3}{4}

or x = -

\frac{2}{3}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given 12x² + 17x + 6 = 0

• 12x² + 17x + 6 = 0

• ( 4x + 3 ) ( 3x + 2 ) = 0

• ( 4x + 3 ) = 0 or ( 3x + 2 ) = 0

∴ x = - $\frac{3}{4}$ or x = - $\frac{2}{3}$

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Factorising

Factorising Question 2 of 10

2. Solve for x : 5x² - 23x - 10 = 0

A. x = 5 or x = - 2

B. x = 5 or x = -

\frac{2}{5}

C. x = 5 or x = -

\frac{5}{2}

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given 5x² - 23x - 10 = 0

• 5x² - 23x - 10 = 0

• ( x – 5 ) ( 5x + 2 ) = 0

• ( x – 5 ) = 0 or ( 5x + 2 ) = 0

∴ x = 5 or x = - $\frac{2}{5}$

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Factorising

Factorising Question 3 of 10

3. Solve for x : 9x² + 5x - 4 = 0

A. x = 1 or x = -

\frac{4}{9}

B. x = - 1 or x =

\frac{4}{9}

C. x = - 1 or x =

\frac{9}{4}

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given 9x² + 5x - 4 = 0

• 9x² + 5x - 4 = 0

• ( x + 1 ) ( 9x – 4 ) = 0

• ( x + 1 ) = 0 or ( 9x – 4 ) = 0

∴ x = - 1 or x = $\frac{4}{9}$

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Factorising

Factorising Question 4 of 10

4. Solve for x : x² - 10x - 56 = 0

A. x = - 4 or x = 14

B. x = 4 or x = - 14

C. x = 2 or x = 28

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given x² - 10x - 56 = 0

• x² - 10x - 56 = 0

• ( x + 4 ) ( x – 14 ) = 0

• ( x + 4 ) = 0 or ( x – 14 ) = 0

∴ x = - 4 or x = 14

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Factorising

Factorising Question 5 of 10

5. Solve for x : 2x² - 33x + 45 = 0

A. x = 15 or x =

\frac{2}{3}

B. x =

\frac{3}{2}

or x = 15

C. x = 3 or x = 5

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given 2x² - 33x + 45 = 0

• 2x² - 33x + 45 = 0

• ( 2x – 3 ) ( x – 15 ) = 0

• ( 2x – 3 ) = 0 or ( x – 15 ) = 0

∴ x = $\frac{3}{2}$ or x = 15

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Factorising

Factorising Question 6 of 10

6. Solve for x : x² - 6x - 91 = 0

A. x = 9 or x = 11

B. x = - 13 or x = 7

C. x = 13 or x = - 7

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given x² - 6x - 91 = 0

• x² - 6x - 91 = 0

• ( x – 13 ) ( x + 7 ) = 0

• ( x – 13 ) = 0 or ( x + 7 ) = 0

∴ x = 13 or x = - 7

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Factorising

Factorising Question 7 of 10

7. Solve for x : 6x³ - 13x² + 5x = 0

A. x = 0 or x =

\frac{1}{2}

or x =

\frac{5}{3}

B. x = 0 or x = 2 or x =

\frac{3}{5}

C. x = 0 or x = 1 or x = 5

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given 6x³ - 13x² + 5x = 0

• 6x³ - 13x² + 5x = 0

• x ( 2x – 1 ) ( 3x – 5 ) = 0

• x = 0 or ( 2x – 1 ) = 0 or ( 3x – 5 ) = 0

∴ x = 0 or x = $\frac{1}{2}$ or x = $\frac{5}{3}$

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Factorising

Factorising Question 8 of 10

8. Solve for x : 5x² - 45 = 0

A. x = - 3 or x = 3

B. x = 5 or x = - 3 or x = 3

C. x = 0 or x = 5

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given 5x² - 45 = 0

• 5x² - 45 = 0

• 5 ( x + 3 ) ( x – 3 ) = 0

• ( x + 3 ) = 0 or ( x – 3 ) = 0

∴ x = – 3 or x = 3

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Factorising

Factorising Question 9 of 10

9. Solve for x : x² + 8 = 0

A. x = 4 or x = 2

B. x = 0 or x = 3

C. x = 3 or x = 2

D. None of the above

Correct Answer
Option D

Detailed Solution

Solution Details

Given x² + 8 = 0

• x² + 8 = 0

• The equation cannot be factorised

∴ There is no solution

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Factorising

Factorising Question 10 of 10

10. Solve for x : $\frac{1}{2}$ x² + $\frac{7}{6}$ x - 1 = 0

A. x = 0 or x =

\frac{1}{2}

B. x =

\frac{2}{3}

or x = - 3

C. x = 2 or x = - 3

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given $\frac{1}{2}$ x² + $\frac{7}{6}$ x - 1 = 0

• $\frac{1}{2}$ x² + $\frac{7}{6}$ x - 1 = 3x² + 7x - 6 = 0

• ( 3x – 2 ) ( x + 3 ) = 0

• ( 3x – 2 ) = 0 or ( x + 3 ) = 0

∴ x = $\frac{2}{3}$ or x = - 3

For more info please see

Factorising

Quiz

Algebra

Factorising

Quiz Quidelines

Quiz

1. Solve for x : 12x 2 + 17x + 6 = 0

2. Solve for x : 5x 2 - 23x - 10 = 0

3. Solve for x : 9x 2 + 5x - 4 = 0

4. Solve for x : x 2 - 10x - 56 = 0

5. Solve for x : 2x 2 - 33x + 45 = 0

6. Solve for x : x 2 - 6x - 91 = 0

7. Solve for x : 6x 3 - 13x 2 + 5x = 0

8. Solve for x : 5x 2 - 45 = 0

9. Solve for x : x 2 + 8 = 0

10. Solve for x : 1 2 x 2 + 7 6 x - 1 = 0

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Quiz Results

Solutions

1. Solve for x : 12x 2 + 17x + 6 = 0

Correct Answer Option C

Detailed Solution

Solution Details

Given 12x 2 + 17x + 6 = 0

• 12x 2 + 17x + 6 = 0 • ( 4x + 3 ) ( 3x + 2 ) = 0 • ( 4x + 3 ) = 0 or ( 3x + 2 ) = 0 ∴ x = - 3 4 or x = - 2 3

2. Solve for x : 5x 2 - 23x - 10 = 0

Correct Answer Option B

Detailed Solution

Solution Details

Given 5x 2 - 23x - 10 = 0

• 5x 2 - 23x - 10 = 0 • ( x – 5 ) ( 5x + 2 ) = 0 • ( x – 5 ) = 0 or ( 5x + 2 ) = 0 ∴ x = 5 or x = - 2 5

3. Solve for x : 9x 2 + 5x - 4 = 0

Correct Answer Option B

Detailed Solution

Solution Details

Given 9x 2 + 5x - 4 = 0

• 9x 2 + 5x - 4 = 0 • ( x + 1 ) ( 9x – 4 ) = 0 • ( x + 1 ) = 0 or ( 9x – 4 ) = 0 ∴ x = - 1 or x = 4 9

4. Solve for x : x 2 - 10x - 56 = 0

Correct Answer Option A

Detailed Solution

Solution Details

Given x 2 - 10x - 56 = 0

• x 2 - 10x - 56 = 0 • ( x + 4 ) ( x – 14 ) = 0 • ( x + 4 ) = 0 or ( x – 14 ) = 0 ∴ x = - 4 or x = 14

5. Solve for x : 2x 2 - 33x + 45 = 0

Correct Answer Option B

Detailed Solution

Solution Details

Given 2x 2 - 33x + 45 = 0

• 2x 2 - 33x + 45 = 0 • ( 2x – 3 ) ( x – 15 ) = 0 • ( 2x – 3 ) = 0 or ( x – 15 ) = 0 ∴ x = 3 2 or x = 15

6. Solve for x : x 2 - 6x - 91 = 0

Correct Answer Option C

Detailed Solution

Solution Details

Given x 2 - 6x - 91 = 0

• x 2 - 6x - 91 = 0 • ( x – 13 ) ( x + 7 ) = 0 • ( x – 13 ) = 0 or ( x + 7 ) = 0 ∴ x = 13 or x = - 7

7. Solve for x : 6x 3 - 13x 2 + 5x = 0

Correct Answer Option A

Detailed Solution

Solution Details

Given 6x 3 - 13x 2 + 5x = 0

• 6x 3 - 13x 2 + 5x = 0 • x ( 2x – 1 ) ( 3x – 5 ) = 0 • x = 0 or ( 2x – 1 ) = 0 or ( 3x – 5 ) = 0 ∴ x = 0 or x = 1 2 or x = 5 3

8. Solve for x : 5x 2 - 45 = 0

Correct Answer Option A

Detailed Solution

Solution Details

Given 5x 2 - 45 = 0

• 5x 2 - 45 = 0 • 5 ( x + 3 ) ( x – 3 ) = 0 • ( x + 3 ) = 0 or ( x – 3 ) = 0 ∴ x = – 3 or x = 3

9. Solve for x : x 2 + 8 = 0

Correct Answer Option D

Detailed Solution

Solution Details

Given x 2 + 8 = 0

• x 2 + 8 = 0

10. Solve for x : 1 2 x 2 + 7 6 x - 1 = 0

Correct Answer Option B

Detailed Solution

Solution Details

Given 1 2 x 2 + 7 6 x - 1 = 0

• 1 2 x 2 + 7 6 x - 1 = 3x 2 + 7x - 6 = 0 • ( 3x – 2 ) ( x + 3 ) = 0 • ( 3x – 2 ) = 0 or ( x + 3 ) = 0 ∴ x = 2 3 or x = - 3

1. Solve for x : 12x² + 17x + 6 = 0

2. Solve for x : 5x² - 23x - 10 = 0

3. Solve for x : 9x² + 5x - 4 = 0

4. Solve for x : x² - 10x - 56 = 0

5. Solve for x : 2x² - 33x + 45 = 0

6. Solve for x : x² - 6x - 91 = 0

7. Solve for x : 6x³ - 13x² + 5x = 0

8. Solve for x : 5x² - 45 = 0

9. Solve for x : x² + 8 = 0

10. Solve for x : $\frac{1}{2}$ x² + $\frac{7}{6}$ x - 1 = 0

1. Solve for x : 12x² + 17x + 6 = 0

Correct Answer
Option C

Given 12x² + 17x + 6 = 0

• 12x² + 17x + 6 = 0

• ( 4x + 3 ) ( 3x + 2 ) = 0

• ( 4x + 3 ) = 0 or ( 3x + 2 ) = 0

∴ x = - $\frac{3}{4}$ or x = - $\frac{2}{3}$

2. Solve for x : 5x² - 23x - 10 = 0

Correct Answer
Option B

Given 5x² - 23x - 10 = 0

• 5x² - 23x - 10 = 0

• ( x – 5 ) ( 5x + 2 ) = 0

• ( x – 5 ) = 0 or ( 5x + 2 ) = 0

∴ x = 5 or x = - $\frac{2}{5}$

3. Solve for x : 9x² + 5x - 4 = 0

Correct Answer
Option B

Given 9x² + 5x - 4 = 0

• 9x² + 5x - 4 = 0

• ( x + 1 ) ( 9x – 4 ) = 0

• ( x + 1 ) = 0 or ( 9x – 4 ) = 0

∴ x = - 1 or x = $\frac{4}{9}$

4. Solve for x : x² - 10x - 56 = 0

Correct Answer
Option A

Given x² - 10x - 56 = 0

• x² - 10x - 56 = 0

• ( x + 4 ) ( x – 14 ) = 0

• ( x + 4 ) = 0 or ( x – 14 ) = 0

∴ x = - 4 or x = 14

5. Solve for x : 2x² - 33x + 45 = 0

Correct Answer
Option B

Given 2x² - 33x + 45 = 0

• 2x² - 33x + 45 = 0

• ( 2x – 3 ) ( x – 15 ) = 0

• ( 2x – 3 ) = 0 or ( x – 15 ) = 0

∴ x = $\frac{3}{2}$ or x = 15

6. Solve for x : x² - 6x - 91 = 0

Correct Answer
Option C

Given x² - 6x - 91 = 0

• x² - 6x - 91 = 0

• ( x – 13 ) ( x + 7 ) = 0

• ( x – 13 ) = 0 or ( x + 7 ) = 0

∴ x = 13 or x = - 7

7. Solve for x : 6x³ - 13x² + 5x = 0

Correct Answer
Option A

Given 6x³ - 13x² + 5x = 0

• 6x³ - 13x² + 5x = 0

• x ( 2x – 1 ) ( 3x – 5 ) = 0

• x = 0 or ( 2x – 1 ) = 0 or ( 3x – 5 ) = 0

∴ x = 0 or x = $\frac{1}{2}$ or x = $\frac{5}{3}$

8. Solve for x : 5x² - 45 = 0

Correct Answer
Option A

Given 5x² - 45 = 0

• 5x² - 45 = 0

• 5 ( x + 3 ) ( x – 3 ) = 0

• ( x + 3 ) = 0 or ( x – 3 ) = 0

∴ x = – 3 or x = 3

9. Solve for x : x² + 8 = 0

Correct Answer
Option D

Given x² + 8 = 0

• x² + 8 = 0

10. Solve for x : $\frac{1}{2}$ x² + $\frac{7}{6}$ x - 1 = 0

Correct Answer
Option B

Given $\frac{1}{2}$ x² + $\frac{7}{6}$ x - 1 = 0

• $\frac{1}{2}$ x² + $\frac{7}{6}$ x - 1 = 3x² + 7x - 6 = 0

• ( 3x – 2 ) ( x + 3 ) = 0

• ( 3x – 2 ) = 0 or ( x + 3 ) = 0

∴ x = $\frac{2}{3}$ or x = - 3