What is the remainder in the synthetic division problem below?

The correct option is A, the remainder is 7.

Explanation:

The coefficient of terms in the given synthetic division are 4,6 an -3.

Write the first coefficient as it is in bottom line.

Now multiply 1 by 4 and write the result (i.e., 4) in middle line below the second coefficient.

Now add 6 and 4 and write the result (i.e., 10 ) in bottom row.

Now multiply 1 by 10 and write the result (i.e., 10) in middle line below the third coefficient.

Now add -3 and 10 and write the result (i.e., 7 ) in bottom row.

Now the first two terms shows the coefficient of polynomial and last term show the remainder.

Since the last term is 7 therefore, the remainder is 7.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."