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pentagon [3]
3 years ago
15

Find the value of c so that (x+2) is a factor of the polynomial p(x)=3x^4-x^2+cx-2

Mathematics
1 answer:
DedPeter [7]3 years ago
4 0
Using polynomial long division, we get
         
         3x^3+6x^2+11x
         _____________
(x+2) | 3x^4-x^2+cx-2
          -(3x^4+6x^3)
          ____________
             6x^3-x^2+cx-2
          - (6x^3+12x^2)
         _____________
        11x^2+cx-2
      -(11x^2+22x) 
       __________
        (22+c)x-2. 

If you're wondering how I did the long division, what I essentially did was get the first value (at the start, it was 3x^4) and divided it by the first value of the divisor (which in x+2 was x) to get 3x^3 in our example. I then subtracted the polynomial by the whole divisor multiplied by, for example, 3x^3 and repeated the process.

For this to be a perfect factor, (x+2)*something must be equal to (22+c)x-2. Focusing on how to cancel out the 2, we have to add 2 to it. To add 2 to it, we have to multiply (x+2) by 1. However, there's a catch, which is that we subtract whatever we multiply (x+2) by, so we have to multiply it by -1 instead. We still need to cross out (22+c)x. Multiplying (x+2) by -1, we get
(-x-2) but by subtracting the whole thing from something means that we have to add -(-x-2)=x+2 to something to get 0. x+2-x-2=0, xo (22+c)x-2 must equal -x-2, meaning that (22+c)=-1 and c=-23
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1 point
Elan Coil [88]

Your current balance if you started the day with $100 in your account is $73

First step is to calculate the total cash at bank

Using this formula

Total Cash at bank= Cash at bank + Deposit

Let plug in the formula

Total Cash at bank=$100+90

Total Cash at bank=$190

Second step is to calculate the amount debited

Debit amount=($60+$3)+($34+$20)

Debit amount=$63+$54

Debit amount=$117

Now let determine your current balance

Current balance=Total cash at bank-Amount debited

Let plug in the formula

Current balance=$190-117

Current balance=$73

Your current balance if you started the day with $100 in your account is $73

Learn more here:

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7 0
2 years ago
Evaluate the expression<br> Show your work <br> b) -10 -5h for h = -6
vazorg [7]

Answer:

20

Step-by-step explanation:

-10-5x(-6)

-10+30

20

4 0
3 years ago
What is the value of x?
andrey2020 [161]

Since this is a parallelogram and the angles are adjacent to one another, a theorem will prove that the sum of these two angles would equal 180°

Therefore, we can set up this equation:

(2x + 24) + x = 180 ⇒ Remove parentheses

2x + 24 + x = 180 ⇒ Combine like terms

3x + 24 = 180 ⇒ Subtract 24 from both sides

3x = 156 ⇒ Divide both sides by 3

x = 52°


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