factor out the greatest common factor from the expression. 18x^7-14x^2
2x^2(9x^5-7)
Factor the expression: 7 + 14x *
To factor out the greatest common factor from the expression 18x^7 - 14x^2, we need to identify the largest factor that both terms share.
First, let's look at the coefficients. The coefficient of 18 is 18, and the coefficient of -14 is 14. The largest number that divides evenly into both 18 and 14 is 2.
Next, let's consider the variables. Both terms have x raised to different exponents: x^7 and x^2. The highest power of x that is common to both terms is x^2.
Therefore, the greatest common factor of 18x^7 and -14x^2 is 2x^2.
To factor it out, divide both terms by the greatest common factor:
(18x^7 - 14x^2) / (2x^2) = 9x^5 - 7
So, after factoring out the greatest common factor, the expression becomes 2x^2(9x^5 - 7).