Factor 3X2 +4X 4 Using the Table Method

Name

Class

Date

Factoring to Solve Quadratic Equations

9-4

Enrichment

You have factored to solve quadratic functions. You can also use a table to convert between the forms ax2 + bx +c and (ax +b)(cx +d).

Factor 3x2 +4x –4 using the table method.

The First Row

The first term in 3x2 + 4x – 4 is 3x2. The third is –4.

Multiplied together, they result in –12x2.

The Right Column

The two remaining empty squares in the column furthest to the right must add up to 4x. These two new terms must multiply to form

–12x2. The terms 6x and –2x will work.

The Second Row

The first box in the second row must contain a factor of 3x2, and the second box must contain a factor of –4. The product of these two factors is 6x. The first term can be 3x, and the second can be 2.

The Last Row

The cells in the last row must be factors of their individual columns, and when multiplied together equal the third box of their row. What factor of 3x2, times what factor of –4, will equal –2x? The terms x and –2 will.

Diagonally down and to the right from 3x is –2. So, the first factor is (3x – 2). Now start at x and look diagonally up and to the right: 2. The second factor is (x + 2). So, 3x2 + 4x – 4 = (3x – 2)(x + 2).

Solve by factoring using the table method.

1. 6x2 – 17x + 12 = 02.x2 + 2x – 3 = 03.–5x2 + 15x + 90 = 0

4.–2x2 + 6x + 56 = 05. x2 + 18x + 80 = 06.x2 + 12x + 20 = 0

Prentice Hall Algebra 1 • Teaching Resources