Tricky Algebra Homework

[SaLoose]

Hello, I have a couple questions for homework that I just don't understand how to do or even how to start.

The questions are:
(1) If p(x-q) ² + r = 2x² - 12x + 5 for all real values of x, find the values of p, q and r.

(2) If (q-p) ² >0 prove that q³ - p³ / pq² - qp² > 3

Any help would be greatly appreciated! Thank you

 

[tkhunny]

(1)
Were you given this problem without being told how to tell if polynomials are identical?

(2)
Are you sure you mean: "q³ - p³ / pq² - qp²"?

Did you intend: "(q³ - p³) / (pq² - qp²)"?

 

[Harry_the_cat]

Should Q2 be "If (q-p)³>0, ..."? ie cubed rather than squared?

Hint for both: Expand out LHS.

 

[Steven G]

Hint: If ax^3+ bx^2-cx + d = 2x^3+ 7x^2+9x - 6, then a=2, b=7, c=-9 and d=-6