Factoring Completely

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

Front

What does GCF stand for?

Back

GCF stands for Greatest Common Factor, which is the largest factor that two or more numbers share.

Front

How do you find the GCF of a set of terms?

Back

To find the GCF, identify the common factors in each term and multiply them together.

Front

Factor the expression: n² + 16n + 63

Back

(n + 7)(n + 9)

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for the Greatest Common Factor (GCF) among the terms.

Front

Factor the expression: 6x⁵y⁴ + 24x⁶y² - 36x³y³

Back

6x³y²(1 + 4x + -6xy) or 6x³y²(4x + 1 - 6xy) depending on the context.

Front

Factor the expression completely: 4k² + 24k + 36

Back

4(k + 3)²

Front

What is a prime polynomial?

Back

A prime polynomial is a polynomial that cannot be factored into simpler polynomials with integer coefficients.

Front

Factor the expression: 3x⁵ - 27x³

Back

3x³(x² - 9) = 3x³(x - 3)(x + 3)

Front

Factor the expression: 12x + 9

Back

3(4x + 3)