Answer:
![P(x)=2x^3-2x^2-49x+48](https://tex.z-dn.net/?f=P%28x%29%3D2x%5E3-2x%5E2-49x%2B48)
Step-by-step explanation:
Let the original polynomial be
.
We know that when it is divided by
, the quotient is
and we get a remainder of 3.
Therefore, this means that:
![\frac{P(x)}{x-5}=2x^2+8x-9+\frac{3}{x-5}](https://tex.z-dn.net/?f=%5Cfrac%7BP%28x%29%7D%7Bx-5%7D%3D2x%5E2%2B8x-9%2B%5Cfrac%7B3%7D%7Bx-5%7D)
Remember what it means when we have a remainder. Say we have 13 divided by 3. Our quotient will be 4 R1, or 4 1 <em>over</em> 3. We put the remainder over the divisor. This is the same thing for polynomials.
So, to find our original polynomial, multiply both sides by
:
![(x-5)\frac{P(x)}{x-5}=(x-5)(2x^2+8x-9+\frac{3}{x-5})](https://tex.z-dn.net/?f=%28x-5%29%5Cfrac%7BP%28x%29%7D%7Bx-5%7D%3D%28x-5%29%282x%5E2%2B8x-9%2B%5Cfrac%7B3%7D%7Bx-5%7D%29)
The left side will cancel. Distribute the right:
![P(x)=2x^2(x-5)+8x(x-5)-9(x-5)+\frac{3}{(x-5)}(x-5)](https://tex.z-dn.net/?f=P%28x%29%3D2x%5E2%28x-5%29%2B8x%28x-5%29-9%28x-5%29%2B%5Cfrac%7B3%7D%7B%28x-5%29%7D%28x-5%29)
Distribute:
![P(x)=(2x^3-10x^2)+(8x^2-40x)+(-9x+45)+(3)](https://tex.z-dn.net/?f=P%28x%29%3D%282x%5E3-10x%5E2%29%2B%288x%5E2-40x%29%2B%28-9x%2B45%29%2B%283%29)
Combine like terms:
![P(x)=(2x^3)+(-10x^2+8x^2)+(-40x-9x)+(45+3)](https://tex.z-dn.net/?f=P%28x%29%3D%282x%5E3%29%2B%28-10x%5E2%2B8x%5E2%29%2B%28-40x-9x%29%2B%2845%2B3%29)
Evaluate:
![P(x)=2x^3-2x^2-49x+48](https://tex.z-dn.net/?f=P%28x%29%3D2x%5E3-2x%5E2-49x%2B48)
And we're done!
Answer: C
3sqrt2
Step-by-step explanation:
Answer:
$24
Step-by-step explanation:
The question being asked is "what is the total that Eric spent on school lunches last month, given that he bought such a lunch 6 times and that each cost $4.
The total amount he spent on school lunches was (6)($4), or $24. Note that this agrees with Eric's $24 estimate.
Answer:
Step-by-step explanation:
B = 2×10⁸
A = 3×10⁸