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Chapter 7: Q. 212 - Exercises (page 850)

How is the 鈥ac鈥 method similar to the 鈥渦ndo FOIL鈥 method? How is it different?

Short Answer

Expert verified

Both the methods "ac"and "undo FOIL" help us factor a trinomial but the difference lies in the leading coefficient. In the "undo FOIL" method the leading coefficient is 1, while the leading coefficient is not equal to 1in the "ac"method.

Step by step solution

01

Step 1. Given Information 

The objective is to write the differences and similarities between 鈥ac鈥 method to the 鈥渦ndo FOIL鈥 method.

02

Step 2. Explanation

In both the methods, we need to find two numbers mand nsuch that they add to the middle term and are the product of the coefficients of the first and the last term.

But the difference lies in the leading coefficient of the trinomial.

The "undo FOIL" method is used only when the leading coefficient of the trinomial is 1that is the trinomial of the form x2+bx+cand then we need to find two numbers mand nsuch that m+n=band mn=c.

But for the "ac"the leading coefficient may not be equal to 1. The trinomial in this method is of the form ax2+bx+cand we find two numbers mandnsuch thatm+n=bandmn=ac.

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