HELP. Multiply the polynomials and simplify the answer. Show your work. (3a³ - 2a - 7) and (4a² - 2a + 1)

Simplify the expression using long division. Show your work.
(2x³ - 10x² + 5x +14) ÷ (x-2)

Part 1)

Part 2)

Step-by-step explanation:

Part 1)

We would like to multiply:

Distribute each term from the first group into the second group. So:

Distribute further:

Combine like terms:

Simplify:

Part 2)

We would like to divide:

Using long division.

Please refer to the attached document.

For the first step, x goes into 2x³ 2x² times. Hence, we multiply our divisor by 2x².

Next, x goes into -6x^2 -6x times. Hence, we multiply our divisor by -6x.

Finally, x goes into -7x -7 times. So, we multiply our divisor by -7 and we simplify.

Therefore:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

there are no choices to this, can you give us some choices so that i can answer it

step-by-step explanation: