Factoring Polynomials by Grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by rearranging and grouping terms to find common factors.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

Front

What is the first step in factoring a polynomial by grouping?

Back

The first step is to group the terms of the polynomial into pairs or sets that have common factors.

Front

Factor the polynomial: 12x^3 - 9x^2 + 4x - 3

Back

(3x^2 + 1)(4x - 3)

Front

Factor the polynomial: 2x^3 + 5x^2 + 6x + 15

Back

(x^2 + 3)(2x + 5)

Front

Factor the polynomial: 3x^3 - 4x^2 + 9x - 12

Back

(x^2 + 3)(3x - 4)

Front

Factor the polynomial: 8x^3 - 64x^2 + x - 8

Back

(8x^2 + 1)(x - 8)

Front

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

Back

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

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

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.