Question

Factorize: x³ + x² - 17x + 15

Answer 1

We have,p(x) = x3 + x2 − 17x + 15
The constant term in p(x) is 15 and its factors are :±1, ±3, ±5, ±15
Put x = 3 in p(x),
we getp(3) = (3)3 + (3)2 − 17(3) + 15
= 27 + 9 − 51 + 15 = 0
so, (x−3) is a factor of p(x).
Put x =1 in p(x),
we getp(1) = (1)3 + (1)2 − 17(1) + 15= 0
so, (x−1) is a factor of p(x)
Put x =−5 in p(x),
we getp(−5) = (−5)3 + (−5)2 − 17(−5) + 15 = 0
so, (x+5) is a factor of p(x).
so, x3 + x2 − 17x + 15 = (x−3)(x−1)(x+5)