FACTORIZATION WORKSHEET QUESTION5

In this page factorization worksheet question5 we are going to see solution of fifth problem.

Step 1:  Arrange the dividend and the divisor according to the descending powers of x and then write the coefficients of dividend in the first zero. Insert 0 for missing terms.

Step 2:  Find out the zero of the divisor.

Step 3:  Put 0 for the first entry in the second row. 

Step 4:  Write down the quotient and remainder accordingly. All the entries except the last one  in the third row constitute the coefficients of the quotient.

Factorization Worksheet Question5

Question 5

Factorize each of the following polynomial x³ - 7 x + 6

Solution

Let p (x) = x³ - 7 x + 6

 x = 1

     p (1) = (1)³ - 7 (1) + 6

             = 1 - 7 + 6

             = 7 - 7

             = 0

So we can decide (x - 1) is a factor. To find other two factors we have to use synthetic division. 

So the factors are (x - 1) and (x² + x - 6). By factoring this quadratic equation we get  (x + 3) (x - 2)

Therefore the required three factors are (x - 1) (x + 3) (x - 2)

(1) Factorize each of the following polynomial x³ - 2 x² - 5 x + 6    Solution

(2) Factorize each of the following polynomial 4 x³ - 7 x + 3  Solution

(3) Factorize each of the following polynomial

 x³ - 23 x² + 142 x - 120    Solution

(4) Factorize each of the following polynomial  4 x³ - 5 x² + 7 x - 6  Solution

(5) Factorize each of the following polynomial x³ - 7 x + 6     Solution

(6) Factorize each of the following polynomial x³  + 13 x² + 32 x + 20   Solution

(7) Factorize each of the following polynomial 2 x³  - 9 x² + 7 x + 6   Solution

(8) Factorize each of the following polynomial x³  - 5 x + 4   Solution

(9) Factorize each of the following polynomial x³ - 10 x² - x + 10   Solution

(10) Factorize each of the following polynomial 2 x³ + 11 x² - 7 x - 6    Solution

(11) Factorize each of the following polynomial x³ + x² + x - 14  Solution

(12) Factorize each of the following polynomial x³ - 5 x² - 2 x + 24   Solution