In this page factorization worksheet question10 we are going to see solution of tenth 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 10**

Factorize each of the following polynomial 2 x³ + 11 x² - 7 x - 6

**Solution**

Let p (x) = 2 x³ + 11 x² - 7 x - 6

x = 1

p (1) = 2 (1)³ + 11 (1)² - 7 (1) - 6

= 2 (1) + 11 (1) - 7 - 6

= 2 + 11 - 13

= 13 - 13

= 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 (2 x² + 13 x + 6). By factoring this quadratic equation we get (x + 6) (2 x + 1)

Therefore the required three factors are (x - 1) (x + 6) (2 x + 1)