Find coeff of x^4 in expansion of x(x^2 + 2x +3)(x^2 +7x - 2)

[Furai]

Ok i've spent some time on this and am stumped, i am not quite sure what sort of method or theorem to use
to answer it correctly except from the fact that there is obviously some form of expanding and simplifying algebra involved.

The question:

Find the coefficient of x^4 in the expansion of

x(x^2 + 2x +3)(x^2 +7x - 2)

I've looked over the binomial theorem but idk if it would be of any relevance to this

A detailed response would be appreciated!

Thank you

 

[Deleted member 4993]

Ok i've spent some time on this and am stumped, i am not quite sure what sort of method or theorem to use
to answer it correctly except from the fact that there is obviously some form of expanding and simplifying algebra involved.

The question:

Find the coefficient of x^4 in the expansion of

x(x^2 + 2x +3)(x^2 +7x - 2)

I've looked over the binomial theorem but idk if it would be of any relevance to this

A detailed response would be appreciated!

Thank you

The only expansion involved here is - multiplying the polynomials and the monomial.

Did you do that (if not - do it now)?

What did you get?

Multiplication is the only route - and take it!

 

[Furai]

The only expansion involved here is - multiplying the polynomials and the monomial.

Did you do that (if not - do it now)?

What did you get?

Multiplication is the only route - and take it!

Am a bit rusty at my math but i assume this is right?

x^3 + 2x^2 + 3x + x^3 + 7x^2 - 2x

That's what i got when i expanded each of the brackets individually by the monomial

 

[Deleted member 4993]

Am a bit rusty at my math but i assume this is right?

x^3 + 2x^2 + 3x + x^3 + 7x^2 - 2x

That's what i got when i expanded each of the brackets individually by the monomial

No ... that is not correct.

x * (x^2 + 2x +3) * (x^2 +7x - 2)

= x * [{x^2 * (x^2 +7x - 2)} + {2x * (x^2 +7x - 2)} + {3 * (x^2 +7x - 2)}] .... multiplying using FOIL

= x* [{x^4 + 7x^3 - 2x^2} + {2x^3 + 14x^2 - 4x} + {3x^2 + 21x - 6}] .... collecting coefficients of similar powers of x

= x * [x^4 + (7x^3 + 2x^3) + (14x^2 - 2x^2 + 3x^2) + (21x - 4x) - 6]

Simplify and do the next set of multiplications and simplify further

 

[pka]

The question:
Find the coefficient of x^4 in the expansion of x(x^2 + 2x +3)(x^2 +7x - 2)

\(\displaystyle x(x^2 + 2x +3)(x^2 +7x - 2)\\ (x^3 + 2x^2 +3x)(x^2 +7x - 2)\\x^5+7x^4-2x^3+2x^4+14x^3-4x^2+3x^3+21x^2-6x\)
See Here
You can finish.

 

[Furai]

I got it thanks.