What is the quotient of (5x2 − 22x + 8) ÷ (x − 4)?

5x - 2

Step-by-step explanation:

We can use synthetic division to find this quotient quickly (but factoring and long division, or even the quadratic formula, would also work).

Setting up synthetic div.:

4  /  5    -22     8

               20    -8

       5      -2     0                  This zero remainder tells us that (5x - 2) is a                  

                                             factor, as is (x - 4).

                                                       (5x2 − 22x + 8)

Thus, (5x2 − 22x + 8) ÷ (x − 4)  =   = 5x - 2 (quotient)

                                                                x - 4

Here we may call the result either "factor" or "quotient".

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

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step-by-step explanation: