Question

The polynomial p(x) = 2x^3+17x^2+41x+30 has a known factor of (x+5)
Rewrite p(x) as a product of linear factors

Answer 1

Answer:

2x³ + 17x² + 41x + 30 =  (x + 5) (x + 2) (2x + 3)

Step-by-step explanation:

2x³ + 17x² + 41x + 30 = (x + 5) (2x² + ax + 6) =

2x³ + (a + 10) x² + (5a + 6) x + 30

a + 10 = 17         a = 7   ( check: 5a + 6 = 5 x 7 + 6 = 41)

2x³ + 17x² + 41x + 30 = (x + 5) (2x² + 7x + 6) = (x + 5) (x + 2) (2x + 3)

Answer 2

Answer:

(x+5)(x+2)(2x+3)

Step-by-step explanation: