Im stuck on the following questions and need some help. Sorry I dont know how to do X squared on the keyboard so X^2 means X squared and etc.
1. Simplify 4X^5 + 16X / 4X
b. Simplify 2X^2 +11X +12 / 2X^2 + X-3
2. Divide X^3 - 5X^2 + X + 10 by X-2
b. Divide X^3 - 27 by X-3
3. (X-2) is a factor of f(X) = X^3 + 7X^2 + qX - 40 therefore find q
4. Show that (2X-1) is a factor of 2X^3 + X^2 + X-1 and then find the quadratic factor.
5. f(X) = X^3 + pX^2 -49X -120 given that f(-5) = 0, find p
b. Factorise f(X) completely into linear factors
6. A function is given as f(X) = aX^3 + bX^2 + X-10. When f(X) is divided by (X-2) the remainder is 36. (X+2) is a factor of f(X), show that a=2 and then find the value for b.
7. A function is given as f(X) = X^3 + aX^2 + bX + 6. Find in terms of a and b, the remainder when f(X) is divided by
then given that these remainders are equal express a in terms of b.
8. Find the remainder when 2X^2 + 4X - 5 is divided by (2X+1)
Sorry I asked for so much, these are past paper questions that I don't understand, so sorry to cause trouble and if you dont mind can you also write out your workings as well to see how to come to that conclusion so I can handle questions of the smilar sort as future reference.
This needs to be in by tomorrow so its in a hurry.
Code:(x^3 - 5x^2 + x + 10) ÷ (x-2) = x^2 - 3x - 5 x^3 - 2x^2 ------------ -3x^2 + x -3x^2 + 6x ----------- -5x + 10 -5x + 10 --------- 0EBCode:(x^3 - 27) ÷ (x-3) = x^2 + 3x + 9 x^3 - 3x^2 ----------- 3x^2 - 27 3x^2 - 9x ---------- 9x - 27 9x - 27 -------- 0
do the long division as usual. The remainder must be zero:
Do #4 the same way as #3.Code:(x^3 + 7x^2 + qx - 40) ÷ (x-2) = x^2+9x+(q+18) x^3 - 2x^2 --------- 9x^2 + qx 9x^2 - 18x ------- (q+18)x -40 (q+18)x - 2q-36 ---------------- 2q - 4 This remainder must be zero: 2q - 4 = 0 ===> q = 2
first plug (-5):
f(-5) = -125 + 25p + 245 - 120 = 0
25p = 0 ==> p = 0
f(x) = x^3 - 49x -120
Split 49 into 24 + 25:
f(x) = x^3 - 25x - 24x - 120
f(x) = x(x^2 - 25) - 24(x+5)
f(x) = x(x+5)(x-5) - 24(x+5)
f(x) = (x+5)(x^2 + 5x -24)
f(x) = (x+5)(x+8)(x-3)
It's very late now. I have to catch some sleep. Sorry that I cann't help you further on.
how about this? i can give you hints as to what to do (the processes for the remaining ones are very similar to what earboth already did), you do them, and tell us your solutions. if they are wrong, someone will tell you why and how to fix it. it will also give you a chance to assess just how much you understood what earboth did
well I will like to do 4,6,7,8 but I don't know how, so hows about you do a step by step for these questions and then I will do a past paper to see if I understood and I will post here if any issues arises.
Sorry I meant to have the same step by step feature like earboth, not actually having the program.
I don't use a special program even though it looks like that.
You can use the [code ] [/code ] tag (but without the blank space in the brackets!) to write a text with equidistance between numbers or signs. So you only have to count the spaces to type terms in exact columns.