Factoring Polynomials and GCF for JAMES

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor a polynomial using the GCF?

Back

To factor a polynomial using the GCF, identify the largest common factor of all terms, then divide each term by the GCF and express the polynomial as the product of the GCF and the resulting polynomial.

Front

Factor the polynomial: 30x^3 + 15x^2 - 18x - 9

Back

3(5x^2 - 3)(2x + 1)

Front

What is the first step in factoring polynomials?

Back

The first step is to look for the GCF of the terms in the polynomial.

Front

Factor the polynomial: -12a^6 + 20a^5 - 4a^4

Back

-4a^4(3a^2 - 5a + 1)

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down a polynomial into its simplest form, where no further factoring is possible.

Front

Factor the polynomial: 12x^2y^4 - 6xy

Back

6xy(2xy^3 - 1)

Front

What is a polynomial?

Back

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

Front

Factor the polynomial: 21x^7y^6 + 30x^5y^8 - 18x^5y^6

Back

3x^5y^6(7x^2 + 10y^2 - 6)

Front

What is the difference between factoring and expanding a polynomial?

Back

Factoring involves breaking down a polynomial into simpler components, while expanding involves multiplying out the components to form the polynomial.