Factoring GCF

Front

What is the definition of the greatest common factor (GCF)?

Back

The greatest common factor (GCF) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder.

Front

How do you find the GCF of two algebraic expressions?

Back

To find the GCF of two algebraic expressions, factor each expression completely and identify the common factors. The GCF is the product of the lowest powers of all common variables and coefficients.

Front

What is the GCF of the coefficients 77, 21, and 49?

Back

The GCF of the coefficients 77, 21, and 49 is 7.

Front

Factor the expression x^5y^2 + x^2y^7z. What is the GCF?

Back

The GCF of the expression x^5y^2 + x^2y^7z is x^2y^2, and the factored form is x^2y^2(x^3 + y^5z).

Front

What is the GCF of 10a^2b^3 and 20a^2b^2?

Back

The GCF of 10a^2b^3 and 20a^2b^2 is 10a^2b^2.

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How do you factor the polynomial 5x^4 - 40x^3 + 10x^2?

Back

To factor the polynomial 5x^4 - 40x^3 + 10x^2, first factor out the GCF, which is 5x^2. The factored form is 5x^2(x^2 - 8x + 2).

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to identify and factor out the greatest common factor (GCF) from all the terms.

Front

What is the GCF of the terms 18x^3, -24x, and -21?

Back

The GCF of the terms 18x^3, -24x, and -21 is 3.

Front

How do you factor the polynomial 18x^3 - 24x - 21?

Back

To factor the polynomial 18x^3 - 24x - 21, first factor out the GCF, which is 3. The factored form is 3(6x^3 - 8x - 7).

Front

What is the significance of factoring in algebra?

Back

Factoring is significant in algebra as it simplifies expressions, solves equations, and helps in finding roots of polynomials.