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Yes, the greatest common factor is less than or equal to the smallest coefficient. For example, the greatest common factor of 38 and 8 is 2.

Q: When finding the greatest common factor of a polynomial can it ever be larger than the smallest coefficient?

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first finding the whole number and then sort them out from least to greatest in answers

You do not necessarily need the common prime factors when finding the greatest common factor, but with large numbers or numbers for which you cannot easily determine all the factors, using prime factorization to determine the greatest common factor is the easiest method. The greatest common factor can then be determined by multiplying the common prime factors together. For example, when trying to find the greatest common factor of 2144 and 5672, finding all their possible factors to compare could be difficult. So, it is easier to find their prime factors, determine the prime factors they have in common, and then multiply the common prime factors to get the greatest common factor. For descriptions and examples of finding the greatest common factor, see the "Related Questions" links below.

That doesn't really exist. A factor tree is a way to notate the process of finding the prime factorization of a given number. The greatest common factor, or GCF, is the largest number that can divide evenly with no remainder into a given set of numbers.

That presumes that math class is not part of the real world, which is debatable. Finding the greatest common factor can help reduce fractions. In a practical, non-academic setting, chefs and carpenters work with fractions and might have need of this skill.

Related questions

Yes.

Evaluating a polynomial is finding the value of the polynomial for a given value of the variable, usually denoted by x. Solving a polynomial equation is finding the value of the variable, x, for which the polynomial equation is true.

The difference depends on what m and n equal. If they are both variable then it dpends on what the equations are for each variable.

Substitute that value of the variable and evaluate the polynomial.

Gcf you use when you are finding the greatest factor for the numbers. Lcm you use when you are finding the smallest multiple in the numbers factors

the smaller number

Distributive

It means finding numbers (constant terms), or polynomials of the same or smaller order that multiply together to give the original polynomial.

The discriminant of the quadratic polynomial ax2 + bx + c is b2 - 4ac.

to investigate change in resistance as temperature is varied

She was afraid it would be constant. (Constance) She was afraid it would be a related function.

The coefficient of restitution is how you quantify bounciness or give bounciness a number, and you do that by dividing the bounce height by the drop height, then finding the square root of that. When you have more bounces you can find more than one coefficient of restitution!