Answer:
-2 3/4
Step-by-step explanation:
i gotchu
Step-by-step explanation:
12 2/5
=144/5
=28/8
Hope this helps!!!
Answer:
a) 2x^4 + 8x^3 + x^2 + 3x
b) evaluate this polynomial at x = 10
Step-by-step explanation:
Hi!
a)
The product of a sum is the sum of the products, having said this:
![(2x^3 + 8x^2 + x + 3) \times x = 2x^4 + 8x^3 + x^2 + 3x](https://tex.z-dn.net/?f=%282x%5E3%20%2B%208x%5E2%20%2B%20x%20%2B%203%29%20%5Ctimes%20x%20%3D%202x%5E4%20%2B%208x%5E3%20%2B%20x%5E2%20%2B%203x)
b)
We can use the result from part a and consider x = 10.
First lets take the first polynomial
![2x^3 + 8x^2 + x + 3 = 2(10)^3 + 8 (10)^2+10^1+3(10)^0](https://tex.z-dn.net/?f=2x%5E3%20%2B%208x%5E2%20%2B%20x%20%2B%203%20%3D%202%2810%29%5E3%20%2B%208%20%2810%29%5E2%2B10%5E1%2B3%2810%29%5E0)
Knowing that every number (excepting probably 0, which could be undefined for some or 1 for others) to the power of 0 is one:
![2x^3 + 8x^2 + x + 3 = 2(1000)+ 8(100)+10+3(1) = 2813](https://tex.z-dn.net/?f=2x%5E3%20%2B%208x%5E2%20%2B%20x%20%2B%203%20%3D%202%281000%29%2B%208%28100%29%2B10%2B3%281%29%20%3D%202813)
Which is the initial number
Now lets conisder the product of the polynomial times x and evaluate it at x=10:
![(2x^3 + 8x^2 + x + 3) \times x = 2x^4 + 8x^3 + x^2 + 3x](https://tex.z-dn.net/?f=%282x%5E3%20%2B%208x%5E2%20%2B%20x%20%2B%203%29%20%5Ctimes%20x%20%3D%202x%5E4%20%2B%208x%5E3%20%2B%20x%5E2%20%2B%203x)
![(2(10)^4 + 8(10)^3 + 10^2 + 3(10) = 2 (10000) + 8(1000) + 100 + 3(10)](https://tex.z-dn.net/?f=%282%2810%29%5E4%20%2B%208%2810%29%5E3%20%2B%2010%5E2%20%2B%203%2810%29%20%3D%202%20%2810000%29%20%2B%208%281000%29%20%2B%20100%20%2B%203%2810%29)
![= 28130](https://tex.z-dn.net/?f=%3D%2028130)
We can now see that teh rule is treu because we can see the whole number as a sum of numbers from 0 to 9 multiplied by a power of 10, and when it is multiplied by 10, each power increases by one, and at the end, the final result is adding a zero at the end