FACTORIZATION WORKSHEET QUESTION12

In this page factorization worksheet question12 we are going to see solution of twelfth 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 Question12

Factorize each of the following polynomial x³ - 5 x² - 2 x + 24

Solution

Let p (x) = x³ - 5 x² - 2 x + 24

x = 1

p (1) = (1)³ - 5 (1)² - 2 (1) + 24

= 1 - 5 - 2 + 24

= 25 - 7

= 18

≠ 0

So we can decide (x - 1) is not a factor.

x = -1

p (-1) = (-1)³ - 5 (-1)² - 2 (-1) + 24

= - 1 - 5 + 2 + 24

= - 6 + 26

= 20

≠ 0

So we can decide (x + 1) is not a factor.

x = 2

p (2) = (2)³ - 5 (2)² - 2 (2) + 24

= 8 - 5 (4) - 4 + 24

= 8  - 20 - 4 + 24

= 32 - 24

= 8

≠ 0

So we can decide (x + 1) is not a factor.

x = -2

p (-2) = (-2)³ - 5 (-2)² - 2 (-2) + 24

= -8 - 5 (4) + 4 + 24

= -8  - 20 + 4 + 24

= - 28 - 28

= 0

So we can decide (x + 2) is a factor. To find other two factors we have to use synthetic division.

factorization worksheet question12

So the factors are (x + 2) and (x² - 7 x + 12). By factoring this quadratic equation we get  (x - 3) (x - 4)

Therefore the required three factors are (x + 2) (x - 3) (x - 4)

(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