## FACTORIZATION WORKSHEET QUESTION3

In this page factorization worksheet question3 we are going to see solution of third 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 Question3

Factorize each of the following polynomial  x³ - 23 x² + 142 x - 120

Solution

Let p (x) =  x³ - 23 x² + 142 x - 120

x = 1

p (1) = 1³ - 23 (1)² + 142 (1) - 120

= 1 - 23 + 142 - 120

= 143 - 143

= 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 - 22 x + 120). By factoring this quadratic equation we get  (x - 12) (x - 10)

Therefore the required three factors are (x - 1) (x - 12) (x - 10)

(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