What is the product of (3a + 2)(4a2 – 2a + 9)?
12a3 − 2a + 18
12a3 + 6a + 9
12a3 − 6a2 + 23a + 18
12a3 + 2a2 + 23a + 18

Option D is correct.

Step-by-step explanation:

Given: polynomials are 3a + 2 and 4a² - 2a + 9

We have to find product.

⇒ ( 3a + 2 ) ( 4a² - 2a + 9 )

= 3a ( 4a² - 2a + 9 ) + 2 ( 4a² - 2a + 9 )

= 3a × 4a² - 3a × 2a + 3a × 9 + 2 × 4a² - 2 × 2a + 2 × 9

= 12a³ - 6a² + 27a + 8a² - 4a + 18

= 12a³ - 6a²+ 8a² - 4a + 27a + 18

= 12a³ + 2a² + 23a + 18

Therefore, Option D is correct.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is