Question

Verify whether (x + 1), (x – 2) and (x + 3) are the factors of the polynomial x3 + 2x2

– 5x – 6 without actual

division. do the steps​

Answer 1

Answer:

Verify whether (x + 1), (x – 2) and (x + 3) are the factors of the polynomial x3 + 2x2

– 5x – 6 without actual

division.

Step-by-step explanation:

pls answer this question urgent

Answer 2

Given Polynomial :

$p(x) = x^3 + 2x^2 - 5x - 6$

To Verify :

(x + 1) is a factor of p(x) if p(— 1) = 0

Now, $p(- 1) = (- 1)^3 + 2 (- 1)^2 - 5(- 1) - 6 = -1 + 2 + 5 - 6 = 0$

Hence, (x + 1) is a factor of p(x).

(x - 2) is a factor of p (x) if p ( 2) = 0

Now, $p ( 2) = (2)^3 + 2 ( 2)^2 - 5 ( 2) - 6 = 8 + 8- 10 - 6 = 0$

Hence, (x - 2) is a factor of p (x).

(x + 3) is a factor of p(x) if p (-3) = 0

Now, $p (-3) = (-3)^3 + 2 (-3)^2 - 5 (-3) - 6 = -27 + 18 + 15 - 6 = 0$

Hence, (x — 3) is a factor of p (x).

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