We can use the Polynomial Remainder Theorem. The PRT states that if we have a polynomial $f(x)$ being divided by a factor in the form of $(x-a)$ , then the remainder of the polynomial is given by $f(a)$ .

We have the polynomial:

$f(x)=3x^{15}-5x^{12}+7x^6-3x^2+12$

And it is being divided by:

$(x+1)$

We can rewrite our factor as:

$(x-(-1))$

Therefore:

$a=-1$

Then our remainder will be:

$f(-1)$

Evaluate:

$\begin{aligned} f(-1)&=3(-1)^{15}-5(-1)^{12}+7(-1)^6-3(-1)^2+12\\&=-3-5+7-3+12\\&=8 \end{aligned}$

So, our remainder will be 8.

4 0

2 years ago

Riya took a train from his hometown to Mumbai . The journey lasted for 3 hrs 35 minutes . The train reached the station at 9:15

zhenek [66]

Answer: 5:40 am

Step-by-step explanation:

The train reached the station at 9:15 am after having travelled for 3 hrs 35 minutes.

The time the train departed from Riya's hometown was the time it arrived in Mumbai station less the time taken to travel:

= 9:15 - 3:35

First deduct the 3 hours:

= 9:15 - 3

= 6 : 15 am

Remove the 35 minutes by first removing the 15 minutes

= 6:15 - 15

= 6:00 am

Then remove the rest of the 35 minutes which is 20 minutes:

= 6:00 - 20 minutes

= 5:40 am

7 0

2 years ago