# Thread: Can anyone help me with these questions

1. ## Can anyone help me with these questions

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.

Show that (2X-1) is a factor of 2X^3 + X^2 + X-1 and then find the quadratic factor.

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.

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

a. (X-2)
b. (X+3)

then given that these remainders are equal express a in terms of b.

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.

Thank You.

2. Well it looks like they want you to use long division for quadratic equations. So it will be slightly difficult to show the work but i'll do my best and try to explain what i'm doing as I go along.

I'll start off just doing one because your going to be using the same procedures for each of the problems so I think if your able to understand one you should be able to do all those problems doing the same work and following these steps.

Find the remainder when 2X^2 + 4X - 5 is divided by (2X+1)

Your first step is to find how many times 2x goes into 2x^2 which is x then multiple x by 1 and you get 2x^2+4x -5
-2x^2-x
You're left with 3x-5 so divide that again by your 2x you get 3/2x so multiple that back through your 2x+1 and you get 3x-5
-3x-3/2

Hopefully that helped its hard to do that on the computer. Try to invision it doing in long division form the key is to just find out how many times the 2x goes into the first term then multiple that back through and then subtract that off so you keep repeating those steps till you have a remainder. Hopefully I'm making sense cause I'm not sure if I am. If you can't figure out the others let me know and i'll show those to you if this helped at all.

You're expected to know the Factor Theorem and the Remainder Theorem.
. . Otherwise, these problems will take all day.

1. Show that (2x-1) is a factor of: .f(x) .= .2x³ + x² + x - 1
and then find the quadratic factor.

If (2x - 1) is a factor of f(x), then: .f(½) = 0.

We have: .f(½) .= .2(½)³ + (½)² + (½) - 1 .= .0 . . . yes!

Use long division and get: .2x³ + x² + x - 1 .= .(2x - 1)(x² + x + 1)

2. A function is given as: .f(x) .= .ax³ + bx² + 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.

If f(x) ÷ (x - 2) has a remainder of 36, then: .f(2) = 36
We have: .a·2³ + b·2² + 2 - 10 .= .36 . . 8a + 4b .= .44 . . 2a + b .= .11 . [1]

If (x + 2) is a factor of f(x), then f(-2) = 0.
We have: .a(-2)³ + b(-2)² + (-2) - 10 .= .0 . . -8a + 4b .= .12 . . -2a + b .= .3 .[2]

Subtract [2] from [1]: .4a = 8 . . a = 2

Substitute into [1]: .2·2 + b .= .11 . . b = 7

4. ## Expressions and Terms

Sorry I dont know how to do X squared on the keyboard so I just used smaller fonts.

Excercise 5.10
1. Write down the index of a in each of the following terms:

a) 6a2 b) 4a3 c) a3
2

d) 5a4b3 e) a2b3c4

5. Originally Posted by Kevin
Sorry I dont know how to do X squared on the keyboard so I just used smaller fonts.

Excercise 5.10
1. Write down the index of a in each of the following terms:

a) 6a2 b) 4a3 c) a3
2

d) 5a4b3 e) a2b3c4