7.4-7.5 Factor Polynomials: GCF & DOS

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 out the GCF from a polynomial?

Back

To factor out the GCF, identify the largest common factor of the terms, then divide each term by the GCF and write it outside the parentheses.

Front

Factor the polynomial: p^2 - 14p

Back

p(p - 14)

Front

What is the process of factoring a polynomial completely?

Back

Factoring completely involves breaking down a polynomial into its simplest factors, ensuring no further factoring is possible.

Front

Factor the polynomial completely: 16x^2 - 32x

Back

16x(x - 2)

Front

What does it mean for a polynomial to be prime?

Back

A polynomial is prime if it cannot be factored into simpler polynomials with integer coefficients.

Front

Factor the polynomial completely: 12x^2 - 36x + 24

Back

12(x^2 - 3x + 2)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern: a^2 - b^2 = (a + b)(a - b).

Front

Can the expression 9n^2 + 1 be factored using the difference of squares?

Back

No, it cannot be factored using the difference of squares.

Front

Factor the polynomial: 4b^5 + 4b^3 + 16b^2

Back

4b^2(b^3 + b + 4)