Factorization Worksheet Question11

In this page factorization worksheet question11 we are going to see solution of seventh 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 11

Factorize each of the following polynomial x³ + x² + x - 14

Solution

Let p (x) = x³ + x² + x - 14

 x = 1

     p (1) = (1)³ + (1)² + (1) - 14

             = 1 + 1 + 1 - 14

             = 3 - 14 

             = -11

             ≠ 0 

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

 x = -1

     p (-1) = (-1)³ + (-1)² + (-1) - 14

             = - 1 + 1 - 1 - 14

             = - 16 + 1

             = -15

             ≠ 0

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

 x = 2

     p (2) = (2)³ + (2)² + (2) - 14 

             = 8 + 4 + 2 - 14

             = 14 - 14

             = 0

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

factorization worksheet question11

So the factors are (x - 2) and (x² + 3 x + 7). We cannot factories this quadratic equation.

Therefore the required factors are (x - 2) and (x² + 3 x + 7)