In this page factorization worksheet question9 we are going to see solution of ninth 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.

Factorize each of the following polynomial x³ - 10 x² - x + 10

**Solution**

Let p (x) = x³ - 10 x² - x + 10

x = 1

p (1) = (1)³ - 10 (1)² - 1 + 10

= 1 - 10 - 1 + 10

= 10 - 10

= 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 - 9 x - 10). By factoring this quadratic equation we get (x - 10) (x + 1)

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

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