Factorization Of Polynomials Using Factor Theorem
- Obtain the polynomial p(x).
- Obtain the constant term in p(x) and find its all possible factors. For example, in the polynomial
x4 + x3 – 7x2 – x + 6 the constant term is 6 and its factors are ± 1, ± 2, ± 3, ± 6.
- Take one of the factors, say a and replace x by it in the given polynomial. If the polynomial reduces to zero, then (x – a) is a factor of polynomial.
- Obtain the factors equal in no. to the degree of polynomial. Let these are (x–a), (x–b), (x–c.)…..
- Write p(x) = k (x–a) (x–b) (x–c) ….. where k is constant.
- Substitute any value of x other than a,b,c …… and find the value of k.
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Factorization Of Polynomials Using Factor Theorem Example Problems With Solutions
Example 1: Factorize x2 +4 + 9 z2 + 4x – 6 xz – 12 z
Example 2: Using factor theorem, factorize the polynomial x3 – 6x2 + 11 x – 6.
Example 3: Using factor theorem, factorize the polynomial x4 + x3 – 7x2 – x + 6.
Example 4: Factorize, 2x4 + x3 – 14x2 – 19x – 6
Example 5: Factorize, 9z3 – 27z2 – 100 z+ 300, if it is given that (3z+10) is a factor of it.
Example 6: Simplify
Example 7: Establish the identity