Edelweiss L.

asked • 11/12/13

chase wants to factor x^2+10x+25 by grouping

chase wants to factor x^2+10x+25 by grouping; however, Paige says it is a special product and can factor a different way. Using complete sentences, explain and demonstrate how both methods will result in the same factors.

1 Expert Answer


Imtiazur S.

Illustrated below is one easy way to factorize a quadratic. The general form of a quadratic expression is

ax2 + bx + c

Split b into two parts such that the product of the two parts equals the value of a * c

For example let's take a = 6, b = 19 and c = 15

a * c = 90

Split b = 19 into two parts which when multiplied yields a * c = 90. Now write the expression again as

6x2 + 9x + 10x + 15

This is equivalent to 3x(2x + 3) + 5(2x + 3). This can now be factored as (3x + 5) * (2x + 3)


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