Question

Finding the greatest common factor of 14x^2+24x^3-16x^6

Answer 1

the greatest common factor is 2x²

Step-by-step explanation:
`\begin{gathered} The\text{ given expression:} \\ 14x^2+24x^3-16x^6 \end{gathered}`

We find the factors common to each of the term. Then we will factorise it out:

`\begin{gathered} 14x^2\text{ = 2 }*\text{ 7 }*\text{ x }*\text{ x} \\ 24x^3\text{ = }2\text{ }*\text{ 2 }*\text{ 2 }*\text{ 3}* x\text{ }* x* x \\ 16x^6=2^{}\text{ }*\text{ 2 }*\text{ 2}*\text{ 2 }* x\text{ }* x* x* x\text{ }* x* x \end{gathered}`
`\begin{gathered} we\text{ check the factors common to all thre}e\text{:} \\ 2\text{ }* x* x=2x^2 \end{gathered}`
`\begin{gathered} 14x^2+24x^3-16x^6\text{ = }2\text{ }x^2(\text{7})\text{ + }2^{}x^2\text{ }*(12x)-2\text{ }x^2(8x^4)\text{ } \\ 14x^2+24x^3-16x^6=2x^2(7+12x-8x^4) \end{gathered}`

Hence, the greatest common factor is 2x²