In this page factorization worksheet question5 we are going to see solution of fifth 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 5
Factorize each of the following polynomial x³ - 7 x + 6
Solution
Let p (x) = x³ - 7 x + 6
x = 1
p (1) = (1)³ - 7 (1) + 6
= 1 - 7 + 6
= 7 - 7
= 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 + x - 6). By factoring this quadratic equation we get (x + 3) (x - 2)
Therefore the required three factors are (x - 1) (x + 3) (x - 2)
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