Factorization Worksheet Question9

In this page factorization worksheet question7 we are going to see solution of ninth 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.

Question 9

Factorize each of the following polynomial x³ - 10 x² - x + 10

Solution

Let p (x) = x³ - 10 x² - x + 10

 x = 1

     p (1) = (1)³ - 10 (1)² - 1 + 10

             = 1 - 10 - 1 + 10

             = 10 - 10

             = 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 - 9 x - 10). By factoring this quadratic equation we get  (x - 10) (x + 1)

Therefore the required three factors are (x - 1) (x - 10) (x + 1)