1 whole should be the answer
Answer:
![(x-1)(2x^2+x+2)](https://tex.z-dn.net/?f=%28x-1%29%282x%5E2%2Bx%2B2%29)
Step-by-step explanation:
Factorize:
![f(x)=2x^3-x^2+x-2](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E3-x%5E2%2Bx-2)
<u>Factor Theorem</u>
If f(a) = 0 for a polynomial then (x - a) is a factor of the polynomial f(x).
Substitute x = 1 into the function:
![\implies f(1)=2(1)^3-1^2+1-2=0](https://tex.z-dn.net/?f=%5Cimplies%20f%281%29%3D2%281%29%5E3-1%5E2%2B1-2%3D0)
Therefore, (x - 1) is a factor.
As the polynomial is cubic:
![\implies f(x)=(x-1)(ax^2+bx+c)](https://tex.z-dn.net/?f=%5Cimplies%20%20f%28x%29%3D%28x-1%29%28ax%5E2%2Bbx%2Bc%29)
Expanding the brackets:
![\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c](https://tex.z-dn.net/?f=%5Cimplies%20%20f%28x%29%3Dax%5E3%2Bbx%5E2%2Bcx-ax%5E2-bx-c)
![\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c](https://tex.z-dn.net/?f=%5Cimplies%20%20f%28x%29%3Dax%5E3%2B%28b-a%29x%5E2%2B%28c-b%29x-c)
Comparing coefficients with the original polynomial:
![\implies ax^3=2x^3 \implies a=2](https://tex.z-dn.net/?f=%5Cimplies%20ax%5E3%3D2x%5E3%20%5Cimplies%20a%3D2)
![\implies (b-a)x^2=-x^2 \implies b-2=-1 \implies b=1](https://tex.z-dn.net/?f=%5Cimplies%20%28b-a%29x%5E2%3D-x%5E2%20%5Cimplies%20b-2%3D-1%20%5Cimplies%20b%3D1)
![\implies -c=-2 \implies c=2](https://tex.z-dn.net/?f=%5Cimplies%20-c%3D-2%20%5Cimplies%20c%3D2)
Therefore:
![\implies f(x)=(x-1)(2x^2+x+2)](https://tex.z-dn.net/?f=%5Cimplies%20%20f%28x%29%3D%28x-1%29%282x%5E2%2Bx%2B2%29)
Cannot be factored any further.
<u>Answer:</u>
24
<u>Step-by-step explanation:</u>
Y is 60% of 40
Equation: Y = P% * X
<u>Solving our equation for Y</u>
Y = P% * X
Y = 60% * 40
<u>Converting percent to decimal:</u>
p = 60%/100 = 0.6
Y = 0.6 * 40
Y = 24
Answer:
![y=\frac{5x}{1+2x^2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5x%7D%7B1%2B2x%5E2%7D)
Step-by-step explanation:
![Option ~A ~ does ~ not ~ have ~a ~ vertical~ asymptote](https://tex.z-dn.net/?f=Option%20~A%20~%20does%20~%20not%20~%20have%20~a%20~%20vertical~%20asymptote)
<u>--------------------------</u>
Hope it helps...
Have a great day!!
Answer:
y=34x+2.625
y=34x+2.75
y=−34x+1.25
y=34x+1.25
y=−34x+2.75
Correct answer:
y=−34x+2.75
Step-by-step explanation: