Year 2 (A-level) Partial Fractions and Algebraic Fractions

Im stuck on a question because I'm not too sure about how to approach it...

Q. Find the values of the constants A, B, C, D and E in the following identity:
5x^4 - 4x^3 + 17x^2 - 5x + 7 = (Ax^2 + Bx +C)(x^2 + 2) + Dx + E

Standard technique would be to start with the RHS, expand the brackets and group like terms (same powers of x) together.

Then since this is an identity, the coefficients of a given power of x will be the same on the right and left of the identity.

This will give you a set of simultaneous equations to solve.

So Ive expanded the RHS and got:
Ax^4 Bx^3 (2A C)x^2 (2 2B D) E

Am I going the right way?

So Ive expanded the RHS and got:
Ax^4 + Bx^3 + (2A + C)x^2 +(2 + 2B + D) + E

Am I going the right way?

Your on the right lines, but you've made some errors there. x^4 down to x^2 terms are correct.

The x and constant terms have errors - I presume the missing x after the parentheses is just a typo.
In particular, where did the "2" by itself come from?

Im stuck on a question because I'm not too sure about how to approach it...
Q. Find the values of the constants A, B, C, D and E in the following identity:
5x^4 - 4x^3 + 17x^2 - 5x + 7 = (Ax^2 + Bx +C)(x^2 + 2) + Dx + E

pretty sure just dividing the rhs by (X^2 + 2) should give you everything in just one step. You'll get the A,B and C and the remainder Dx + E