Greatest Common Factor in Polynomials

Front

What is the greatest common factor (GCF) of two polynomials?

Back

The GCF of two polynomials is the highest degree polynomial that divides both polynomials without leaving a remainder.

Front

How do you find the GCF of numerical coefficients in polynomials?

Back

To find the GCF of numerical coefficients, list the factors of each coefficient and identify the largest factor that appears in both lists.

Front

What is the GCF of the polynomials 15a^2b^2c - 25ab^2c^2?

Back

5ab^2c

Front

How can the GCF be used in simplifying polynomial expressions?

Back

The GCF can be factored out from each term in the polynomial, simplifying the expression.

Front

What is the GCF of the polynomials 30a^2bc^2 - 50ab^2c?

Back

10a^2bc

Front

Explain how the GCF can help in optimizing material usage in construction.

Back

By finding the GCF of dimensions, construction companies can minimize waste and ensure efficient use of materials.

Front

What is the GCF of the polynomials 20a^3b^2 - 30a^2b^3?

Back

10a^2b^2

Front

How do you factor out the GCF from the expression 12x^3y^2 - 18x^2y^3?

Back

Factor out 6x^2y^2 from both terms.

Front

What is the GCF of the polynomials 18x^2y^2 - 27xy and 36x^3y - 54x^2y^2?

Back

9xy(2x - 3y)

Front

Define the term 'polynomial'.

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.