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 standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, such as ax^n + bx^(n-1) + ... + k.

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means breaking it down into irreducible factors, which cannot be factored further over the set of real numbers.

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: 9x^2 + 9x - 10

Back

(3x + 5)(3x - 2)

Front

Factor the polynomial: 3v^2 - 4v - 7

Back

(3v - 7)(v + 1)

Front

Factor the polynomial: k^2 - 2k - 24

Back

(k + 4)(k - 6)

Front

Factor the polynomial: x^2 - 49

Back

(x + 7)(x - 7)

Front

Factor completely: 81m^2 - 1

Back

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