In this page factorization worksheet question7 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
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
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)