Question

(x^4)(x^-2)= what?

Answer 1

when multiplying exponential expressions with the same base, you add the exponents


so...


(x^4)*(x^-2) = x^(4+(-2)) = x^(4-2) = x^2


giving the final answer of x^2

Answer 2

Thank you, i didn't know if they was trying a trick question or not.

Answer 3

well it's sort of a trick question as they threw in the negative when you're adding (ie the negative turns the addition problem into a subtraction problem)

Answer 4

but it looks like you know what you're doing, so it's not much of a trick

Answer 5

So P^4*P^-5*P would equal P ?

Answer 6

oh wait, made a typo...

Answer 7

P^4*P^-5*P = P^4*P^-5*P^1 = P^(4-5+1) = P^0 = 1

Answer 8

So the end result is just 1

Answer 9

Well i have answer P & answer 1 so which one would i pick?

Answer 10

The answer is 1 because anything to the zeroth power (except 0) is 1

Answer 11

So for x^-9*x^-7*x^5 that would be 1/x^11 right?

Answer 12

Exactly, you nailed it. Nice job.

Answer 13

Ok thank you. Can you help me with this: Factor Completely. 10x^3-8x^2=6x

Answer 14

10x^3-8x^2=6x


10x^3-8x^2-6x = 0


2x(5x^2-4x-3) = 0 ... Here we're factoring out the GCF 2x


Now let's try to factor 5x^2-4x-3. Multiply the first and last values: 5*(-3) = -15


Now we must look for two numbers that both multiply to -15 and add to -4.


It turns out that there are no such numbers (rational numbers at least). So 5x^2-4x-3 can't be factored (over the rationals)


Basically, 10x^3-8x^2-6x completely factors to 2x(5x^2-4x-3)

Answer 15

im so sorry i must of hit the wrong button. its suppose to be +6x at the end.

Answer 16

oh, then the final answer is 2x(5x^2-4x+3) ... the -3 becomes +3

Answer 17

Ok thank you so much. What about this:
Choose the binomial or trinomial that is a factor of the given polynomial.
4x^2+13x+3

Answer 18

4x^2+13x+3


4x^2+12x+x+3 .... See note below


(4x^2+12x)+(x+3)


4x(x+3)+1(x+3)


(4x+1)(x+3)


So the factors are 4x+1 and x+3


Note: We multiply the first and last value 4 and 3 to get 12. We then look for two numbers that multiply to 12 and add to 13. They are 12 and 1. So 13x = 12x+x

Answer 19

I have these answers to choose from:
(4x+1) (2x+1) (2x+3) (4x+3) so would it be the 1st one and the last one?

Answer 20

No, just the first one as the last one is NOT the same as x+3