Factoring Polynomials Completely

Front

Define factoring in algebra.

Back

Factoring in algebra 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

Factor the polynomial: 4x^3 - 4x^2 - 5x + 5.

Back

(x-1)(4x^2-5)

Front

Factor the polynomial: 6x^2 + 5x - 6.

Back

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

Front

Simplify the expression: (3x + 5)(3x^2 - 4x - 2).

Back

9x^3 + 3x^2 - 26x - 10

Front

Factor the difference of squares: 81x^2 - 16.

Back

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

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 the polynomial: x^4 - 9x^2.

Back

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

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for a common factor in all terms.