Question

Factor out the greatest common factor of 28x²+4x⁴-16x³.

Answer 1

To factor out the greatest common factor from the polynomial 28x²+4x⁴-16x³, we find that the GCF is 4x². Dividing each term by 4x² gives the factored expression 4x²(7 + x² - 4x).

Step-by-step explanation:

The question asks to factor out the greatest common factor (GCF) from the polynomial 28x²+4x⁴-16x³. To find the GCF of the coefficients 28, 4, and 16, we notice that the largest number that divides all of them is 4. Additionally, the smallest exponent of x present in all terms is 2, so x² is the greatest common factor in terms of x.

Now we factor out the GCF:

• The term 28x² is divided by 4x² to yield 7.
• The term 4x⁴ is divided by 4x² to give x².
• The term -16x³ is divided by 4x² to yield -4x.

So the expression factored out by the greatest common factor is 4x²(7 + x² - 4x).