In this page factorization worksheet question7 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.

Factorize each of the following polynomial 2 x³ - 9 x² + 7 x + 6

**Solution**

Let p (x) = 2 x³ - 9 x² + 7 x + 6

x = 1

p (1) = 2 (1)³ - 9 (1)² + 7 (1) + 6

= 2 - 9 + 7 + 6

= 9 - 9 + 6

= 6

≠ 0

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

x = -1

p (-1) = 2 (-1)³ - 9 (-1)² + 7 (-1) + 6

= - 2 - 9 - 7 + 6

= - 16 + 6

= -10

≠ 0

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

x = 2

p (2) = 2 (2)³ - 9 (2)² + 7 (2) + 6

= 16 - 36 + 14 + 6

= 36 - 36

= 0

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

So the factors are (x - 2) and (2 x² - 5 x - 3). By factoring this quadratic equation we get (x - 3) (2 x + 1)

Therefore the required three factors are (x - 2) (x - 3) (2 x + 1)

(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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