By taking out the common factor, how can 4x² + 28x = 0 be written?
Answer and explanation
Correct answer: 4x(x + 7) = 0
The governing concept is common-factor extraction, in which the greatest factor shared by every term is placed outside parentheses. Both 4x² and 28x contain 4x. Dividing 4x² by 4x leaves x, while dividing 28x by 4x leaves 7. The plus sign remains plus, so the factorised expression is 4x(x + 7). Expanding it verifies the result: 4x(x + 7) = 4x² + 28x. Therefore option A is correct. Option B loses the factor x and expands to 4x + 28, not the original expression. Options C and D use a minus sign, which would produce a negative 28x term. The factorisation can also lead to solving the equation through the zero-product property.
Frequently asked questions
What is the correct answer to this question?
4x(x + 7) = 0
Why is this the correct answer?
The governing concept is common-factor extraction, in which the greatest factor shared by every term is placed outside parentheses. Both 4x² and 28x contain 4x. Dividing 4x² by 4x leaves x, while dividing 28x by 4x leaves 7. The plus sign remains plus, so the factorised expression is 4x(x + 7). Expanding it verifies the result: 4x(x + 7) = 4x² + 28x. Therefore option A is correct. Option B loses the factor x and expands to 4x + 28, not the original expression. Options C and D use a minus sign, which would produce a negative 28x term. The factorisation can also lead to solving the equation through the zero-product property.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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