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 two or more numbers or expressions share. It is used to simplify expressions before factoring.

Front

How do you factor a quadratic polynomial of the form ax^2 + bx + c?

Back

To factor a quadratic polynomial, find two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the middle term using these numbers and factor by grouping.

Front

What is the difference of squares?

Back

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

Front

Factor the polynomial: x^2 - 25

Back

(x + 5)(x - 5) - This is an example of the difference of squares.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, such as a^2 + 2ab + b^2 = (a + b)^2.

Front

Factor the polynomial: x^2 + 10x + 25

Back

(x + 5)(x + 5) or (x + 5)^2 - This is a perfect square trinomial.

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.

Front

Factor the polynomial: 2x^3 + 4x^2 + 2x

Back

2x(x^2 + 2x + 1) or 2x(x + 1)^2 - This uses factoring by grouping.