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Murljashka [212]
3 years ago
13

P(x)=2x^4-x^3+2x^2-6. What is the remainder when P(x) is divided by (x-2)?

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
4 0

Answer: 26

Step-by-step explanation: From the remainder theorem ,

If P (x) = 2x⁴ ⁻ x³ + 2x² ⁻ 6. is divided by ( x - 2 ).

It means that if P(x) is divided by (x - 2 ) and leaves a Remainder, it implies that x - 2 is not a factor of P(x) , but if it leaves no remainder, it means x-2 is a factor of P(x).

Therefore , to find the remainder, find the zero of x - 2, and substitutes for the value in P(x)  to know the remainder

x - 2 = 0

x = 2

Now put this in P(x)

P(x) = 2(2)⁴ - (2)³ + 2(2)² - 6

= 2(16) -8 + 2(4) -6

= 32 -8 +8 -6

=26

Therefore the remainder when P(x) is divided by x -2

=26

Note: Since the division of P(x) by x - 2 leaves a remainder, it means that

x - 2 ≠ a factor of P(x)

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Hector has a part-time job at a garage. He gets a paycheck of $820 every for
ElenaW [278]

Answer:

<u>A. Hector pays $ 123 in taxes each paycheck.</u>

<u>B.  Hector should expect to receive $615 or 75% of his regular pay.</u>

<u>C. Hector will be paid $ 902 when he receives his next 4- week paycheck.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the questions correctly:

Paycheck Hector gets every four weeks = $ 820

2. Hector has to pay 15% of his income in taxes. How much money does he

pay in taxes each paycheck? Show your thinking with a diagram and

calculations.

Taxes = 15% of 820

Taxes = 0.15 * 820

Taxes = $ 123

Hector's paycheck: ←------------------------------820--------------------------------------→

Taxes:                       ←----123---→

3. Hector took a 1-week vacation, so his next paycheck will only be for 3

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receive? How much is that?

We can answer this question using the Direct Rule of Three, this way:

  Weeks         Paycheck

      4                   820

      3                     x

***********************************

4x = 820 * 3

4x = 2,460

x = 2,460/4

x = 615

615/820 = 0.75 = 75%

4. The garage owner is impressed with Hector's work and is giving him a

10% raise. How much will Hector be paid when he receives his next 4- week paycheck?

Raise = 10% of 820

Raise = 0.1 * 820 = 82

Next 4- week paycheck = 820 + 82 = 902

4 0
3 years ago
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