Choose the correct form of (6x^2+15x) after taking out the common factor.
Answer and explanation
Correct answer: (3x(2x+5))
A common factor is a factor present in every term. The terms are \\(6x^2\\) and \\(15x\\). Both are divisible by 3 and both contain \\(x\\), so the common factor \\(3x\\) can be taken outside the parentheses. Dividing each term by \\(3x\\) leaves \\(2x\\) and 5.
Thus \\(6x^2+15x=3x(2x+5)\\), which is option A. Multiplying back gives \\(3x\cdot2x+3x\cdot5=6x^2+15x\\), confirming the factorisation. Option B omits the common factor \\(x\\), option C does not simplify the expression, and option D uses 5 as a factor even though 6 is not divisible by 5.
Frequently asked questions
What is the correct answer to this question?
(3x(2x+5))
Why is this the correct answer?
A common factor is a factor present in every term. The terms are \\(6x^2\\) and \\(15x\\). Both are divisible by 3 and both contain \\(x\\), so the common factor \\(3x\\) can be taken outside the parentheses. Dividing each term by \\(3x\\) leaves \\(2x\\) and 5.
Thus \\(6x^2+15x=3x(2x+5)\\), which is option A. Multiplying back gives \\(3x\cdot2x+3x\cdot5=6x^2+15x\\), confirming the factorisation. Option B omits the common factor \\(x\\), option C does not simplify the expression, and option D uses 5 as a factor even though 6 is not divisible by 5.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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