For example: Factor You have Multiply ac which, in this problem is Find two numbers whose product is and whose sum is One number is positive and the other is negative because we want the product to be negative. The positive factor has a higher absolute value because we want the sum to be positive. We start the list: the sum is not +7 the sum is not +7 the sum is not +7 the sum is not +7 the sum is not +7 the sum is not +7 7 is not a factor the sum is 7 Write replacing with Now factor by grouping:
The "factoring box" is a technique for grouping factors. To use this box, you must first take out any factor that is common to all 3 terms. If we had started with we would have to first factor out the 4 to get Place the first and last terms in the main diagonal (upper left and lower right). Then, insert the two terms we discovered above, -8x and +15x, in the remaining two locations.
Notice that each row has common factors and each column has common factors has common factor 3x and has common factor 2x We'll write those factors on a new first row and a new left column:
The factors are the top row and the left column:
Using a different box If we had put the -8x and 15x in the other 2 places.