Factoring Polynomials

Front

What is 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 that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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 difference of squares?

Back

A difference of squares can be factored using the formula: a^2 - b^2 = (a + b)(a - b).

Front

Factor the polynomial: 8x^3 - 1

Back

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

Front

Factor the polynomial completely: 169 - 9x^2

Back

-1(3x + 13)(3x - 13)

Front

What is the formula for factoring a perfect square trinomial?

Back

A perfect square trinomial can be factored using the formula: a^2 + 2ab + b^2 = (a + b)^2 or a^2 - 2ab + b^2 = (a - b)^2.

Front

Factor the polynomial: 3x^2 - 75

Back

3(x + 5)(x - 5)

Front

Factor the polynomial completely: 2x^2 + 7x + 6

Back

(2x + 3)(x + 2)

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.