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

Question

Mathematics

Alejandro Cisneros

17 February, 20:16

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

+4

Answers (1)

Know the Answer?

Ariella Andrews · Answer 1

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)

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

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