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दम्भो दर्पोऽभिमानश्च क्रोध: पारुष्यमेव च |अज्ञानं चाभिजातस्य पार्थ सम्पदमासुरीम् ||

Factoring by Grouping with a Grid Box

Factoring by Grouping with a Grid Box

Factoring-Trinomials-1

Let’s look at factoring

Factoring-by-Grouping-1

This time, let’s use our grouping process written in a grid box.

When “factoring by grouping”, dealing with the signs may be problematic. To avoid this confusion, many students find the creation of a “grid box” to be helpful.

We start, again, by multiply the leading coefficient, a, and the constant term, c.

10 • (-6) = -60

2.

We still consider all of the possible factors of this new product and we find the one pair that adds to the middle term’s coefficient, b. For this example, we need a sum of -11.

4 + -15 = -11

Factors of -60:

(1) • (-60)

(2) • (-30)

(3) • (-20)

(4) • (-15)

(5) • (-12)

(6) • (-10)

(10) • (-6)

(12) • (-5)

(15) • (-4)

(20) • (-3)

(30) • (-2)

(60) • (-1)

Factoring-by-Grouping-2

Notice what happens in this example which contains a common factor of 2, that has not been factored out before starting the process.

Factoring-by-Grouping-3

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