Answer :
Final answer:
The greatest common factor of the expression 3x⁴ -15x³+21x² is 3x². When we factor out 3x² from each term, we get the factored expression 3x²(x² - 5x + 7).
Explanation:
To factor out the greatest common factor from the expression 3x⁴ -15x³+21x², we first need to identify the greatest common factor of each term. The coefficients 3, -15, and 21 have a common factor of 3. Additionally, every term includes a variable x with an exponent, and the smallest exponent is 2. So, the greatest common factor is 3x².
Subtracting the exponent of the greatest common factor from the exponent of each term, we obtain the following expressions: x² for the first term, x for the second, and no variable x for the third. Then, divide each coefficient by 3, we get: 1 for the first term, -5 for the second term, and 7 for the third term.
So when we factor out the greatest common factor from the original expression 3x⁴ -15x³+21x², we get: 3x²(x² - 5x + 7).
Learn more about Factoring Expressions here:
https://brainly.com/question/34538238
#SPJ11
