Factoring polynomials

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 is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, typically in the form (a ± b)² = a² ± 2ab + b².

Front

Factor the polynomial: w³ + 3w.

Back

w(w² + 3).

Front

What is the formula for finding the missing value 'c' in a perfect square trinomial?

Back

The missing value 'c' can be found using the formula c = (b/2)², where b is the coefficient of the x term.

Front

Factor the difference of squares: 81m² - 1.

Back

(9m - 1)(9m + 1).

Front

What is the difference of squares?

Back

The difference of squares is a special product that states a² - b² = (a - b)(a + b).

Front

Factor the polynomial: 8r³ + 16r².

Back

8r²(r + 2).

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 trinomial of the form x² + bx + c?

Back

To factor a trinomial of this form, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n), where m and n are those two numbers.