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Greeley [361]
2 years ago
15

Using the remainder theorem which quotient has a remainder of 20?

Mathematics
1 answer:
stealth61 [152]2 years ago
3 0

Answer:

D

Step-by-step explanation:

When a polynomial f(x) is divided by (x - a) then remainder is f(a)

A

divided by (x + 4 ), then a = - 4

(-4)^{4} - 8(- 4)² + 16 = 256 - 128 + 16 = 144 ≠ 20

B

divided by (x - 2), then a = 2

3(2)³ + 7(2)² + 5(2) + 2

= 3(8) + 7(4) + 10 + 2

= 24 + 28 + 12 = = 64 ≠ 20

C

divided by (x + 5) , then a = - 5

(- 5)³ + 5(- 5)² - 4(- 5) + 6

= - 125 + 125 + 20 + 6 = 26 ≠ 20

D

divided by (x - 2), then a = 2

3(2)^{4} - 5(2)³ + 5(2) + 2

= 3(16) - 5(8) + 10 + 2

= 48 - 40 + 12 = 20 ← Remainder of 20

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