What is the factorised form obtained by taking the common factor from \(3x^4+9x^3\)?
Answer and explanation
Correct answer: \(3x^3(x+3)\)
The greatest common factor of \(3x^4\) and \(9x^3\) is \(3x^3\). Taking it outside gives \(3x^4+9x^3=3x^3(x+3)\), since \(3x^3\times x=3x^4\) and \(3x^3 imes3=9x^3\). Option C is not a valid factorisation because factoring out 9 would require a fractional coefficient in the bracket, not \(x+1\). Exam tip: multiply the factor outside the bracket by every term inside to verify the result.
Frequently asked questions
What is the correct answer to this question?
\(3x^3(x+3)\)
Why is this the correct answer?
The greatest common factor of \(3x^4\) and \(9x^3\) is \(3x^3\). Taking it outside gives \(3x^4+9x^3=3x^3(x+3)\), since \(3x^3\times x=3x^4\) and \(3x^3 imes3=9x^3\). Option C is not a valid factorisation because factoring out 9 would require a fractional coefficient in the bracket, not \(x+1\). Exam tip: multiply the factor outside the bracket by every term inside to verify the result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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