Question

Can you help me solve the polynomial function? (college algebra)
y=x^3+10x^2+3x-126

Answer 1

y = (x + 7) (x + 6) (x − 3)

Explanation:

Using rational root theorem, possible rational roots are:

±1, ±2, ±3, ±6, ±7, ±9, ±14, ±18, ±21, ±42, ±63, ±126

Using trial and error, we find that +3 is one of the roots.

There are 3 ways to continue from here: continue using trial and error to look for other rational roots; use long division to factor; or use grouping.

Using grouping:

y = x³ + 10x² + 3x − 126

y = x³ + 10x² − 39x + 42x − 126

y = x (x² + 10x − 39) + 42 (x − 3)

y = x (x + 13) (x − 3) + 42 (x − 3)

y = (x (x + 13) + 42) (x − 3)

y = (x² + 13x + 42) (x − 3)

y = (x + 7) (x + 6) (x − 3)