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Answer on Algebra Question for hailey

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Question #12158
Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.

Let&#039;s factor the trinomial x&sup2; + bx + c. We know that if b&sup2;-4c &gt;= 0 then this trinomial has zeros and it can be factorized. It&#039;s zeros are

x1 = [ -b + &radic;(b&sup2;-4c) ] / 2

and

x2 = [ -b - &radic;(b&sup2;-4c) ] / 2.

So, we can factor it as

x&sup2; + bx + c = (x-x1)(x-x2).

In a case of trinomial ax&sup2; + bx + c we can factorize it as

ax&sup2; + bx + c = a(x&sup2; + b/a&middot;x + c/a),

where the trinomial x&sup2; + b/a&middot;x + c/a has the same form as x&sup2; + bx + c.