Trinomials of the Form x

Trinomials of the Form x - 6 Example 2 Factor x 2 – 7 x...

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Trinomials of the Form x^2 + bx + c To factor polynomials of the form  x 2  +  bx  +  c , begin with two pairs of parentheses with  x  at the left of  each.   (  x   )(  x   )  Next, find two integers whose product is  c  and whose sum is  b  and place them at the right of the  parentheses.  Example 1 Factor  x 2  + 8  x  + 12.  x 2  + 8  x  + 12 = (  x   )(  x   )  12 can be factored in a variety of ways:  (1)(12), (–1)(–12), (2)(6), (–2)(–6), (3)(4), (–3)(–4) Only one of those pairs of factors sum to 8, namely (2)(6), so  x 2  + 8  x  + 12 = (  x  + 2)(  x
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Unformatted text preview: + 6) Example 2 Factor x 2 – 7 x – 18. –18 can be factored in the following ways: (1)(–18), (–1)(18), (2)(–9), (–2)(9), (3)(–6), (–3)(6) The only combination whose sum is also –7 is (2)(–9), so x 2 – 7 x + 18 = ( x + 2)( x – 9) Example 3 Factor x 2 – 6 x + 9. 9 can be factored as (1)(9), (–1)(–9), (3)(3), (–3)(–3) The only combination whose sum is –6 is (–3)(–3), so x 2 – 6 x + 9 = ( x – 3)( x – 3) = ( x – 3) 2...
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