Factoring Polynomials Completely

Front

Define Factoring in Mathematics

Back

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

Front

What is a Polynomial?

Back

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

Front

What does it mean to Factor a Polynomial Completely?

Back

Factoring a polynomial completely means expressing it as a product of irreducible polynomials, meaning it cannot be factored further over the given number system.

Front

What is the Difference of Squares Formula?

Back

The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).

Front

Factor Completely: x^4 - 9x^2

Back

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

Front

What is the Greatest Common Factor (GCF)?

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

Front

How to Factor by Grouping?

Back

To factor by grouping, divide the polynomial into groups, factor out the GCF from each group, and then factor out the common binomial factor.

Front

Factor Completely: 5x^2 + 5x - 10

Back

5(x + 2)(x - 1)

Front

What is a Quadratic Polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax^2 + bx + c, where a, b, and c are constants.

Front

Factor Completely: 81x^2 - 16

Back

(9x + 4)(9x - 4)