Maths Questions Pretty Please..?

Question

Could anyone please help me out, with the full working out and solution to each problem. thanks

QUESTION 2) Use the remainder theorem to find the remainder when 2x^4 - x^2 + 3x - 2 is divided by (2x-1)

QUESTION 3) When x^4 + ax^2 + bx - 2 is divided by (x-1) the remainder is -2, and when it is divided by (x+1) the remainder is -6. Find the values of a and b.

QUESTION 5) The polynomial x^3 +px^2+6 is exactly divisible by (x+2) and (x-3). Find the values or p and q.

QUESTION 7) If x^3 + 4x^2 - 3x +2 = (x+1)(ax^2+bx+c) + d for all the values of x, find the values of a,b,c, and d.

QUESTION 8) If x^3 + 4x^2 - 12x + 14 = x^3 + (mx + n)^2 + 5 for all the values of x, find the values of m and n.

QUESTION 9) If x^2 = a(x+2)^2 + b(x+2) + c for all values of x, find the values of a,b,c.

THANKS HEAPS IN ADVANCE..

hey.. ops QUESTION 5 is wrong.. sorry its missing the q...

5) x^3 + px^2 + qx + 6 loll...

Answer 1

2) The remainder theorem does not apply here; it only works when the divisor is in the form "x-r" where r is a constant. In this case you just have to use long division:
(2x^4 - x^2 + 3x -2)/(2x-1) = x^3 - 1/2x^2 - 1/4x - 9/8 remainder = 7/8

3) The remainder theorem applies here because the two divisors are both in the form "x - r". To find the remainder you substitute "r" in for "x". This results in the remainder. Make that equal to the remainder that is given and solve the system of equations...
Ans: Substituting the first r (= 1) into the dividend, we get "a + b = -1". Now, substituting the second r (= -1) into the dividend, we get "a - b = -5". Solving the resulting system of equations, we get (a,b) = (-7/2, 3/2).

5) You seem to be missing a "q" in the original equation, as it appears in your answer. I am assuming that instead of "6" you meant "6q", which is the logical place for the variable. If a polynomial f(x) is exactly divisible by "x - r", then f(r) = 0. Using this principle, we see that "2p+3q=4". Also, "3p+2q=-9". Solving the resulting system of equations we get (p,q)=(6,-7).

Now, unfortunately I have to go eat supper. If you want more help please feel free to contact me at [e-mail], or IM me at wigglyworm91 if I am available.

I'll check if you wrote back after supper.

Answer 2

DUDE!!!! MAYBE IF YOU'D PAY ATTENTION IN MATH CLASS YOU WOULD BE SMART!!!!