Let p(x) = x3 + 13x2 + 32x + 20 ± 2, ± 4, ± 5 …… By trial method,
p(−1) = (−1)3 + 13(−1)2 + 32(−1) + 20
= − 1 +13 − 32 + 20
= 33 − 33 = 0
As p(−1) is zero, therefore, x + 1 is a factor of this polynomial p(x).
Let us find the quotient on dividing x3 + 13x2 + 32x + 20 by (x + 1).
By long division,
It is known that,
Dividend = Divisor × Quotient + Remainder
x3 + 13x2 + 32x + 20 = (x + 1) (x2 + 12x + 20) + 0
= (x + 1) (x2 + 10x + 2x + 20)
= (x + 1) [x (x + 10) + 2 (x + 10)]
= (x + 1) (x + 10) (x + 2)
= (x + 1) (x + 2) (x + 10)
