Mathematics: :polonymal : question : find a,b and c. 2x^3 +3x^2 -4x -5 = a(x+1)^3 +b(x+1)^2 +c(x+1) for explaining

:polonymal : question : find a,b and c. 2x^3 +3x^2

Ответ:

brysong19

16.01.2022

Expand the right hand side, simplify, and match up the coefficients of same-power terms.

a(x+1)^3+b(x+1)^2+c(x+1)=a(x^3+3x^2+3x+1)+b(x^2+2x+1)+c(x+1)

Since this must be the same as 2x^3+3x^2-4x-5

, you need to satisfy

$\begin{cases}a=2\\3a+b=3\\3a+2b+c=-4\\a+b+c=-5\end{cases}$

The solution for

is already given, a=2

. Substitute this into the second equation to find

.

$3a+b=3\implies 6+b=3\implies b=-3$

Now plug a,b

into either remaining equation to find

.

$a+b+c=-5\implies 2-3+c=-5\implies c=-4$

And just to check that the third equation is also satisfied,

$3a+2b+c=-4\implies 6-6-4=-4\checkmark$

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Ответ:

haleylayne74

17.12.2021

Mathematics

about 137 degrees

Step-by-step explanation:

see attached picture

I am not sure how to solve this could anyone help???

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:polonymal :

question : find a,b and c.

2x^3 +3x^2 -4x -5 = a(x+1)^3 +b(x+1)^2 +c(x+1)

for explaining

Ответ:

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