What will be obtained by factoring 9x² − 27x = 0?
Answer and explanation
Correct answer: 9x(x − 3) = 0
The governing concept is taking the greatest common factor from every term of a polynomial. In 9x² − 27x, both terms contain 9x. Dividing each term by 9x gives x and −3 respectively, so the expression becomes 9x(x − 3). Therefore the factored equation is 9x(x − 3) = 0, making option A correct. A quick expansion verifies it: 9x multiplied by x gives 9x², and 9x multiplied by −3 gives −27x. Option B incorrectly omits the factor x, option C changes the sign of the constant term, and option D also has the wrong sign. The factor form can then be used with the zero-product property to find x = 0 or x = 3.
Frequently asked questions
What is the correct answer to this question?
9x(x − 3) = 0
Why is this the correct answer?
The governing concept is taking the greatest common factor from every term of a polynomial. In 9x² − 27x, both terms contain 9x. Dividing each term by 9x gives x and −3 respectively, so the expression becomes 9x(x − 3). Therefore the factored equation is 9x(x − 3) = 0, making option A correct. A quick expansion verifies it: 9x multiplied by x gives 9x², and 9x multiplied by −3 gives −27x. Option B incorrectly omits the factor x, option C changes the sign of the constant term, and option D also has the wrong sign. The factor form can then be used with the zero-product property to find x = 0 or x = 3.
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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