In this page factorization worksheet question6 we are going to see solution of sixth 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 + 13 x² + 32 x + 20

**Solution**

Let p (x) = x³ + 13 x² + 32 x + 20

x = 1

p (1) = (1)³ + 13 (1)² + 32 (1) + 20

= 1 + 13 + 32 + 20

= 66

≠ 0

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

x = -1

p (-1) = (-1)³ + 13 (-1)² + 32 (-1) + 20

= -1 + 13 - 32 + 20

= - 33 + 33

= 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 + 12 x + 20). By factoring this quadratic equation we get (x + 10) (x + 2)

Therefore the required three factors are (x + 1) (x + 10) (x + 2)

(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

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