There is a factoring shortcut when the first term is x2. If the second sign is plus, choose the factors whose sum is the coefficient of the second term. For example the factors of 6 we need for x2 – 7x + 6 need to sum to 7: x2 – 7x + 6 = (x – 1)(x – 6). The factors of 6 we need for x2 + 5x + 6 need to sum to 5: x2 + 5x + 6 = (x + 2)(x + 3).
If the second sign is minus, the difference of the factors needs to be
the coefficient of the middle term. If the first sign is plus, the bigger
factor will have the plus sign. If the first sign is minus, the bigger factor
will have the minus sign.
Examples
x2 + 3x –
10: The factors of 10 whose difference is 3 are 2 and 5. The first sign is
plus, so the plus sign goes with 5, the bigger factor: x2 + 3x – 10 =
(x + 5)(x – 2).
x2 – 5x –
14: The factors of 14 whose difference is 5 are 2 and 7. The first sign is
minus, so the minus sign goes with 7, the bigger factor:
Practice
Solutions
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