(Nov. 19, 2024) 4th block: Factoring Polynomials Using GCF

Front

What does GCF stand for in the context of polynomials?

Back

GCF stands for Greatest Common Factor, which is the largest polynomial that divides each term of a polynomial without leaving a remainder.

Front

How do you find the GCF of two or more monomials?

Back

To find the GCF of two or more monomials, identify the common factors in the coefficients and the variables, taking the lowest power of each variable.

Front

What is the GCF of the monomials 6x^3 and 9x^2?

Back

The GCF is 3x^2.

Front

What is the first step in factoring a polynomial using GCF?

Back

The first step is to identify the GCF of all the terms in the polynomial.

Front

Factor the polynomial 12x^4 + 8x^3 - 4x^2 using GCF.

Back

The factored form is 4x^2(3x^2 + 2x - 1).

Front

What is the GCF of the polynomial 20x^5 + 15x^3 - 5x?

Back

The GCF is 5x.

Front

How can you verify that you have factored a polynomial correctly using GCF?

Back

You can verify by distributing the GCF back into the factored form to see if you obtain the original polynomial.

Front

What is the GCF of the polynomial 18a^4b^2 - 12a^3b^3 + 6a^2b?

Back

The GCF is 6a^2b.

Front

What is the GCF of the polynomial 25x^4 - 10x^3 + 5x?

Back

The GCF is 5x.

Front

Explain why finding the GCF is important in factoring polynomials.

Back

Finding the GCF simplifies the polynomial and makes it easier to factor further or solve equations.