FACTORING POLYNOMIALS

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler 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 does it mean to factor completely?

Back

Factoring completely means breaking down a polynomial into its simplest factors, such that no further factoring is possible.

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers or expressions share.

Front

How do you find the GCF of 4x and 6?

Back

The GCF of 4x and 6 is 2, so you can factor it as 2(2x + 3).

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 expression: x^2 - 9.

Back

x^2 - 9 = (x + 3)(x - 3) (difference of squares).

Front

What is a perfect square trinomial?

Back

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

Front

Factor the expression: 4k^2 + 24k + 36.

Back

4k^2 + 24k + 36 = 4(k + 3)^2 (perfect square trinomial).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.