Factoring by Grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors together, allowing for easier factorization.

Front

What is the first step in factoring by grouping?

Back

The first step is to rearrange the polynomial into two groups that can be factored separately.

Front

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

Back

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

Front

Factor the Polynomial: 63x^3 + 54x^2 - 105x - 90

Back

3(3x^2 - 5)(7x + 6)

Front

Factor the Polynomial: 12x^3 + 4x^2 + 3x + 1

Back

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

Front

Factor the Polynomial: 96x^3 - 84x^2 + 112x - 98

Back

2(6x^2 + 7)(8x - 7)

Front

Factor the Polynomial: 16x^2 + 48x

Back

16x(x + 3)

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

How do you check if your factorization is correct?

Back

You can check your factorization by multiplying the factors back together to see if you obtain the original polynomial.

Front

What is the significance of the leading coefficient in polynomials?

Back

The leading coefficient is the coefficient of the term with the highest degree and it affects the end behavior of the polynomial.