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Factoring quadratics of the form x2 + bx + c ?
This tutorial will help you factor quadratics that look something like this: x2 + 7x + 12
(Positive coefficients; no leading coefficient.)
Step 1: Write down all the different ways to factor the constant coefficient (12) into two whole numbers:12 = 1 * 1212 = 2 * 612 = 3 * 4(Order doesn't matter. So 3 * 4 is the same as 4 * 3.) Step 2: Now, for each possible factorization, add together the two factors. You're looking for two that add up to the middle coefficient, which is 7.
1 + 12 = 132 + 6 = 83 + 4 = 7 < --------------------------- found it!The factors which worked out were 3 and 4, so here's how you factor the polynomial:(x + 3)(x + 4) Step 3: Check your answer by multiplying out using FOIL:(x + 3)(x + 4) = x2 + 7x + 12.
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Proof of the Properties of vector arithmetic Proof of a(v → + w → ) = av → + aw → We will begin with the two vectors, v → = (v 1 , v 2 ,..., v n )and w? = w
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