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)