# Thread: help with exponents and polynomials

1. ## help with exponents and polynomials

Hey there! these are some questions that I am having some trouble with. They are probably easy for most people, but I am aboslutely horrendous so any and all help would be excellent! Thank you!

1) (3x - 5)^4
2) (4x2y6z)^2 (-x5y7z8)^6
3) 4x^4 - 4x^3 + 3x^2 - 5x +2 (divided by) 2x-3

Thanks again!

2. Originally Posted by kushmonster

1) (3x - 5)^4
Use the binomial theorem to expand this one.

Here's a tute you can read.

Exponents

You may want to re-write the second question, it's a shambles!

Originally Posted by kushmonster

3) 4x^4 - 4x^3 + 3x^2 - 5x +2 (divided by) 2x-3

Have you been taught polynomial long division?

Read this Polynomial Long Division

3. Originally Posted by kushmonster
Hey there! these are some questions that I am having some trouble with. They are probably easy for most people, but I am aboslutely horrendous so any and all help would be excellent! Thank you!

1) (3x - 5)^4
2) (4x2y6z)^2 (-x5y7z8)^6
3) 4x^4 - 4x^3 + 3x^2 - 5x +2 (divided by) 2x-3

Thanks again!
Hi kushmonster,

(1) $(3x-5)^4$

Could be broken down into $(3x-5)(3x-5)(3x-5)(3x-5)$. Then you can multiply 2 pieces at a time using the distributive property. Multiply the first two binomials , then the last two. Then use distribution to multiple the 2 trinomials together. There's also a binomial expansion you could use, but I don't know if you've been there yet.

$(9x^2-30x+25)(9x^2-30x+25)$

Can you finish the job?

(2) $(4x^2y^6z)^2(-x^5y^7z^8)^6$

Remember your rules! When taking a power to a power, you multiply exponents.

$(16x^4y^{12}z^2)(-x^{30}y^{42}z^{48})$

When multiplying bases, you add exponents. Now, can you finish?

(3) Use synthetic or polynominial division as Pickslides suggested for this on.

Good luck.

4. well I'm not really sure what you want to do with question (1), I presume multiply it...

If so then (3x-5)^4 = (3x-5)(3x-5)(3x-5)(3x-5)
= 3x(3x-5)-5(3x-5)(3x-5)(3x-5)
= (9x^2 - 30x +25)(9x^2 - 30x +25)
= 9x^2(9x^2 - 30x +25) -30x(9x^2 - 30x +25) +25(9x^2 - 30x +25)

I take it you can finish it from here

(2) Practically the same as Q1

(3) This is straight forward long division, refer to your text book. It's quite easy really