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Near the beginning of Lesson 5.3 , a strategy for factoring trinomials of the form x 2 + bx + c was developed by exploring the product of the...
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Near the beginning of Lesson 5.32

, a strategy for factoring trinomials of the form x + bx + c was developed by exploring the product of the binomials ( x + p ) and ( x + q ).

a. Explain how the development of this factoring strategy is an example of working backwards to solve a problem. 

b. The product of ( x + p)( x + q ) can be written as x2 + ( p + q )x + pq.

An intermediate step in this multiplication is x2 + px +qx + pq = x2 + b ( p + q )x + pq.

Explain why px + qx = ( p + q )x


c) Explain why the expression x2 + (p + q )x + pq leads to the need to determine integers that add to b and have a product c when factoring a trinomial of the form x2 + bx + c.

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