Which of the following expressions is this one equivalent to? (x^4-2x^3+x-2)÷(x^3+1) a.) x^2-x+1 b.) x^2+3x+2 c.) x^2+1 d.) x-2

Hello from MrBillDoesMath!

Choice D,  x-2

Discussion:

Observe the the highest order term in the numerator is  x^4 and the highest order term in the denominator is x^3. So the highest order term in their quotient is x^4/x^3 = x.  Choice D is the only possible answer as all other choices start with x^2

Regards,  

MrB

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

i got 10.28 but that rounds up to 10.3