If the polynomial f (x) can be non-zero polynomial g (x) is divisible, that you can find a polynomial q (x), so f (x) = q (x) · g (x), then g (x) is called f (x) of a result type. Of course, when q (x) is f (x) of a result type, and q (x), g (x) are not greater than the number of f (x) the number of times.
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Note decomposition due to decomposition of the factor is defined by the method mentioned common factor method ⑴ ⑵ group decomposition formula method ⑶ ⑷ demolition items, make items with cross-multiplication method ⑸ ⑹ application for type Theorem Note g (x) ≠ 0, but q (x) can be equal to 0 (when f (x) = 0 hours). A few can also be seen as a result of type. Demand due to decomposition is defined by a polynomial type of process is called decomposition by type, also known as factoring. Can be calculated directly, or use formula. Commonly used formula: a ^ 2-b ^ 2 = (a + b) (ab) (a + b) ^ 2 = a ^ 2 +2 ab + b ^ 2 (ab) ^ 2 = a ^ 2-2ab + b ^ 2 a ^ 3 + b ^ 3 = (a + b) (a ^ 2-ab + b ^ 2). a ^ 3-b ^ 3 = (ab) (a ^ 2 + ab + b ^ 2) Decomposition method ⑴ mention the factor common factor method ① common factor: all contain a common type is called this because the common factor of the polynomial. ② to mention common factor method: In general, if a common factor of the polynomial can be mentioned in brackets out this common factor, the product of the polynomial written in the form of the factor, because this type of decomposition method is called to mention common factor method. am + bm + cm = m (a + b + c) ③ specific methods: When the coefficients are integers, the common factor of the coefficient should take the greatest common divisor of the coefficients; letters take the same letter, and the letters Take the lowest index number if the first polynomial is negative, generally that 2-b ^ 2 = (a + b) (a-b) ② completely square formula: a ^ 2 ± 2ab + b ^ 2 = (a ± b) ^ 2 ※ able to use full square formula decomposed by type of polynomial must be tri- polynomial,[url=http://www.buy-ugg.us/][b]title=UGGS Outlet[/b][/url], of which two can be written as two numbers (or type) and the square of the form, another is that the two numbers (or type) the product of 2 times. ③ cubic and formulas: a ^ 3 + b ^ 3 = (a + b) (a ^ 2-ab + b ^ 2). cubic difference formula: a ^ 3-b ^ 3 = (ab) (a ^ 2 + ab + b ^ 2). ④ completely cubic equation: a ^ 3 ± 3a ^ 2b +3 ab ^ 2 ± b ^ 3 = (a ± b) ^ 3 ⑤ a ^ nb ^ n = (ab) [a ^ (n-1) + a ^ (n-2) b + ... ... + b ^ (n-2) a + b ^ (n-1)] a ^ m + b ^ m = (a + b) [a ^ (m-1)-a ^ (m-2) b + ... ...-b ^ (m-2) a + b ^ (m-1)] (m is odd) ⑶ packet decomposition group decomposition method: to a polynomial group, then decomposed by type of method. Packet decomposition must have a clear purpose, that is grouped, you can directly mention the use of common factor or formula. ⑷ demolition items, fill term method split entry, fill entry method: to a certain polynomial on each other apart, or to fill In contrast the number of two (or more), so that the original style suitable to mention common factor method, using the formula method or group decomposition decomposition; to note that the polynomial must be equal to the original principles of the deformation. ⑸ Cross phase multiplication ① x ^ 2 + (p + q) x + pq type factorization formula quadratic trinomial of these features are: quadratic coefficient is 1; constant term is the product of two numbers; a coefficient is a constant factor of two and. Therefore, we can direct some of the quadratic coefficient is a quadratic trinomial factoring: x ^ 2 + (p + q) x + pq = (x + p) (x + q) ② kx ^ 2 + mx + n-type formula for the factor decomposition if we can be decomposed into k = ac, n = bd, and there is ad + bc = m, then kx ^ 2 + mx + n = (ax b) (cx d) a -----/ b ac = k bd = n c / ----- d ad + bc = m ※ polynomials of general steps: ① If there are common factor of the polynomial, then the first mentioned common factor; ② If the there is no common factor, you can try to use the formula to multiply the cross-phase decomposition; ③ If the above method does not break down,[url=http://www.moncler-online.us/][b]title=Moncler Jackets[/b][/url], you can try to use groups, split entry, make entry method to decompose; ④ broken down by type, must be a polynomial for every type It can no longer break up. ⑹ apply the factor theorem if f (a) = 0, then f (x) must contain the factor (xa). If f (x) = x ^ 2 +5 x +6, f (-2) = 0, can be determined (x +2) is x ^ 2 +5 x +6 a result type. Further reading: 1Baidu know http://zhidao.baidu.com
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