By taking out the common factor, how can 5x² + 15x = 0 be written?
Answer and explanation
Correct answer: 5x(x + 3) = 0
The governing algebraic principle is taking out a common factor from every term while preserving the original expression. Both terms, 5x² and 15x, contain 5x. Dividing the first term by 5x gives x, and dividing the second term by 5x gives 3. Therefore 5x² + 15x = 5x(x + 3), so the equation becomes 5x(x + 3) = 0. Expanding this expression returns 5x² + 15x, confirming the result. Option B omits the common factor x and therefore cannot reproduce the original quadratic term. Option C has an incorrect negative sign, while option D also changes the plus sign to minus. Thus option A is the unique correct form.
Frequently asked questions
What is the correct answer to this question?
5x(x + 3) = 0
Why is this the correct answer?
The governing algebraic principle is taking out a common factor from every term while preserving the original expression. Both terms, 5x² and 15x, contain 5x. Dividing the first term by 5x gives x, and dividing the second term by 5x gives 3. Therefore 5x² + 15x = 5x(x + 3), so the equation becomes 5x(x + 3) = 0. Expanding this expression returns 5x² + 15x, confirming the result. Option B omits the common factor x and therefore cannot reproduce the original quadratic term. Option C has an incorrect negative sign, while option D also changes the plus sign to minus. Thus option A is the unique correct form.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
