find the remainder for each of the following using the remainder theorem
(x⁴-10x³+2x²-8x+5)÷(x-10)
(x³+4x²+3x-2)÷x-3
(3x²-5x+4)÷(x-3)​


Sagot :

Answer:

1.) 125

2.) 70

3.) 16

Explanation:

We have to use as you said the Remainder theorem

Solution:

1.) (x⁴-10x³+2x²-8x+5)÷(x-10) Substitute 10 for x

(10)⁴ - 10(10)³ + 2(10)² - 8(10) + 5 Multiply

10,000 - 10,000 + 200 - 80 + 5

= 125 ⬅ Remainder

2.) (x³+4x²+3x-2)÷x-3 Substitute 3 for x

(3)³ + 4(3)² + 3(3) - 2 Multiply

27 + 36 + 9 - 2

= 70 ⬅ Remainder

3.) (3x²-5x+4)÷(x-3) Substitute 3 for x

3(3)² - 5(3) + 4 Multiply

27 - 15 + 4

= 16 ⬅ Remainder

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