## 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

x^{4}+ x^{3}– 7x^{2}– 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 x^{2} +4 + 9 z^{2} + 4x – 6 xz – 12 z

**Solution:**

**Example 2: ** Using factor theorem, factorize the polynomial x^{3} – 6x^{2} + 11 x – 6.

**Solution:**

**Example 3: **Using factor theorem, factorize the polynomial x^{4} + x^{3} – 7x^{2} – x + 6.

**Solution:**

**Example 4: **Factorize, 2x^{4} + x^{3} – 14x^{2} – 19x – 6

**Solution:**

**Example 5: **Factorize, 9z^{3} – 27z^{2} – 100 z+ 300, if it is given that (3z+10) is a factor of it.

**Solution:**

**Example 6: **Simplify

**Solution:**

**Example 7: **Establish the identity

**Solution:**