Question

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

Answer 1

the greatest common factor is 2x²

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