Question

. If x + 2 is a factor of x3 + ax2 + 11x + 6, find
the value of a.
​

Answer 1

given :- x + 2 a factor of x³ + ax² + 11x + 6

equating x + 2 with 0

➡ x + 2 = 0

➡ x = -2

we know that remainder is 0 when any polynomial is divided by it's factor.

therefore p(-2) = (-2)³ + a(-2)² + 11(-2) + 6 = 0

➡ -8 + 4a - 22 + 6 = 0

➡ -8 - 22 + 6 + 4a = 0

➡ -24 + 4a = 0

➡ 4a = 24

➡ a = 24/4

➡ a = 6

verification :-

= -24 + 4(6)

= -24 + 24

= 0

hence, the value of a is 6

Answer 2

Step-by-step explanation:

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