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Tcecarenko [31]
3 years ago
10

Please answer

Mathematics
1 answer:
Allushta [10]3 years ago
5 0

ANSWER

The correct answer is C.

EXPLANATION

The given polynomial has equation

p(b) =  {b}^{3}  + 3 {b}^{2}  - b + 12

According to the Remainnder Theorem, if (b+4) is a factor of p(b) = b³+3b²-b+12 then

p( - 4) = 0

We now substitute b=-4 to check.

p( - 4) =  {( - 4)}^{3}  + 3 {( - 4)}^{2} - ( - 4) + 12

p( - 4) =   - 64+ 48  + 4 + 12

Simplify:

p( - 4) =  - 16 + 16 = 0

Since p(-4) is zero, (b+4) is a factor of p(b) = b³+3b²-b+12.

The correct choice is C.

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