Answer:
Part A
a·(a² - a + 1) + 5·a = a³ - a² + 6·a
Part B
The value of a·(a² - a + 1) + 5·a, for a = -2 is -24
Step-by-step explanation:
Part A
The given function is a·(a² - a + 1) + 5·a
The function is simplified by expanding the product of sums into sums of products, as follows;
a·(a² - a + 1) + 5·a = a × a² - a × a + a × 1 + 5·a = a³ - a² + a + 5·a = a³ - a² + 6·a
The function, a·(a² - a + 1) + 5·a, in simplified format is therefore;
a·(a² - a + 1) + 5·a = a³ - a² + 6·a
Part B
When a = -2, we get;
(a³ - a² + 6·a) = (-2)³ - (-2)² + 6·(-2) = -8 - 4 - 12 = -24
Answer: See the diagram below.
This diagram shows a closed filled in circle at -14 on the number line. Also, the shaded region is to the left of the closed circle. This visually represents values that are smaller than -14, or equal to -14.
The filled in circle is used to indicate "include this endpoint". In contrast, an open hole indicates "do not include this endpoint" which is only used if the inequality was instead of
. The "or equal to" portion is why we include the endpoint.
