Question

I'm solving polynomial inequalities and I need to know (-4-x)(x+7)(x-3) > 0

Answer 1

Given the inequalities

(-4 -x)(x+7)(x-3) >0

Step 1: Find the zeros of the polynomials

For (-4 -x)

`\begin{gathered} (-4-x)=0 \\ -4\text{ -x =0} \\ -x=4 \\ x\text{ = -4} \end{gathered}`

For (x+7)

`\begin{gathered} x\text{ +7 = 0} \\ x\text{ = 0 - 7} \\ x\text{ = -7} \end{gathered}`

For (x-3)

`\begin{gathered} x-3\text{ =}0 \\ x\text{ = 0+ 3} \\ x\text{ = 3} \end{gathered}`

Step 2: Draw the range of values on a number line

Step 3: Construct a table to test the range

The table tests the ranges that were obtained from the number line

column 1 shows the range

The values are then tested for each range.

Column 6 shows the product of all the values gotten

The solution to the polynomial is that which was accepted

Since the inequality sign is that of a greater sign, we will accept those that are positive

Hence the solution is

[tex]\begin{gathered} x\text{ < -7 } \\ \text{and} \\ -4