Question

The polynomial p(x)=2x^3-x^2-25x-12 has a known factor of (x+3). Rewrite p(x) as a product of linear factors.

P(x)=?

Answer 1

p(x) = (x + 3) (2x + 1) (x − 4)

Explanation:

One way to find the other factor is long division (see attached).

Another way is to multiply x + 3 by ax² + bx + c, then match the result to p(x).

(x + 3) (ax² + bx + c)

ax³ + bx² + cx + 3ax² + 3bx + 3c

ax³ + (b+3a)x² + (c+3b)x + 3c

a = 2, b = -7, c = -4

Therefore:

p(x) = (x + 3) (2x² − 7x − 4)

Factoring:

p(x) = (x + 3) (2x + 1) (x − 4)