Question

WILL GIVE BRAINLIEST!!


Given 5x3+8x2−7x−6.

1) The binomial (x+2) is a factor of the polynomial expression. Describe how you know it is a factor.

2) The binomial (x+1) is NOT a factor of the polynomial expression. Explain how you know it is not a factor.

Answer 1

given a polynomial with factor (x - a)

Then x = a is a root of the polynomial and f(a) = 0

(1)

(x+ 2) is a factor , hence x = - 2 is a root

Evaluate the polynomial for x = - 2

f(- 2) = 5(- 2)³ + 8(- 2)² - 7(- 2) - 6 = - 40 + 32 + 14 - 6 = 0

Hence (x + 2 ) is a factor

(2)

If (x + 1) is a factor then x = - 1 is a root

5(- 1)³ + 8(-1)² - 7(- 1) - 6 = -5 + 8 + 7 - 6 = 4

Since f( - 1) ≠ 0

Then (x + 1) is not a factor